














t 



Class _ 

Book _ 



COPYRIGHT DEPOSIT 

























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SURVEYOR’S TRANSIT 



























































CALDWELL’S 


PRACTICAL 


1 


LAND SURVEYING 


OR 


Up JM of jlunmjing @;ibe 


Adapted to the Use of Schools, Private Students, 
and Practical Surveyors. 


/ BY 

M. P. CALDWELL, 

» 

Author of Caldwell’s Arithmetic, and County Surveyor 
of Hall County, Georgia, 



J. W. BURKE COMPANY. 

1880. 






Entered according to Act of Congress, in the year 1880, by 
M. P. CALDWELL. 

In the Office of the Librarian of Congress, at Washington. 









VO 

HON. «T. B. ESTES. 

TOE 

FRIEND OF MY BOYHOOD, AN I'VDEVIaTIVG FRIEND THROUGH LIFE, 

AND A 

GREAT LOVER OF SCIENCE, 

THTS 


▼OLCME la RESPECTFULL! DEDICATED. 



PREFACE 


L AND is the foundation of the whole wealth of the world. Land 
surveying is, therefore, a most important and useful branch of 
study, and as an art is indispensable in carrying on many of the 
ordinary transactions of life. It is exceedingly desirable to be an 
accurate and accomplished Surveyor. In this fast age , when 
everything is done in a hurry, it becomes necessary to adopt the 
plan and methods which will give the student the greatest amount 
of useful knowledge in the shortest time and for the smallest outlay 
of money, that he may be thus practically prepared for the duties 
of life. Thousands of young men have not the time nor means to 
devote to a long course of preparation for surveying, and are de¬ 
sirous of gaining such a practical knowledge as will enable them 
to survey, map and estimate land in the shortest way possible. 
This volume has been prepared for that very large class of stu¬ 
dents as well as for the common schools and Practical Surveyors 
of the country. The want of such a work on Surveying is very 
generally felt by educators and private students, and it is hoped this 
want will now be met and supplied. Here the student will fiijd the 
experience of twenty-five years in so small a compass as that a few 
weeks of pleasant study will prepare him to run land, plat and es¬ 
timate it, and make his maps with ease and precision. 

The Author is greatly indebted to Professor Williams Ruther¬ 
ford, A. M., Professor of Mathematics, University of Georgia, who 
has had long experience as a Practical Surveyor, for many, very 
many valuable hints, and much assistance in the preparation of 
this work, as well as for several important chapters from his pen 
in the body of the book. 

The Appendix is a rich one. For the first time ever printed the 
student has the reason why the magnetic needle stands North and 



PREFACE. 


South, from the pen of that wonderful scientist, Dr. Alexander 
Means, of Emory College, Oxford, Ga., in a learned chapter on 
the “ Polarity of the Needle.’’ 

County Surveyors will be greatly interested and instructed by the 
chapter on their duties and synopsis of the law binding on them, 
from J. B. Estes, Attorney and Counselor at Law, Gainesville, 
Georgia. 

The carefully prepared chapter on Texas Land System and Sur¬ 
veying, is from Col. Warren Douglas, of Cleburne, Texas, an 
old official and experienced Surveyor of that State. This chapter 
will be peculiarly interesting to all students, and at once adapts 
my book to Texas schools and students as well as to those of other 
States. 

Impartial criticism is invited by the Author, that future editions 
may be made more and more perfect and desirable. 

M. P. C. 

Gainesville , Ga., November , 1880. 



NOTICE TO THE PUBLIC. 


This work on Surveying is turned over to J. W. Burke & Co. 
Macon, Ga., who will publish it in fine style and supply the trade. 
They are also the publishers of Caldwell’s Practical Arithmetic, 
which is commanding an extensive sale and should be in the 
bands of every one who studies this work, as it will be found to bta 
a valuable assistant in mastering the beautiful study of Surveying. 

The Author. 


t 






mtptj 


CHAPTER I.—Definitions. 


S URVEYING is the art of running lines with a com¬ 
pass, taking measurements with a chain and platting 
and calculating the area. 

A line is extension without breadth or thickness. 

A right or straight line is the shortest line that can be 
drawn between two points. 

A curved line is one that bends in all its parts. 

Parallel lines are such as are equally distant from each 
other running the same direction. 

A crooked line is one composed of several straight lines, 
joined to one another, extending in different directions. 

When the word line is used it means a straight one un¬ 
less defined otherwise. 

The bearing of the line is the angle the line makes with 
the direction of the needle. 

A point is position without dimensions. 

The extremities of a line are points. 

The deflection of a line is the turning from the true or 
straight course. 

Surface is that which has extension in length and breadth 
without thickness. 

A plane surface is a level or even surface. 

Area is the amount of surface expressed in squares of 
any given denomination—as square inches, square feet, 
yards, rods, etc. 



10 


LAND SURVEYING. 


An angle is the inclination or opening of two lines 
which meet at a point. 

A right angle is one formed by a base line and 
a perpendicular one to it. 

An acute angle is one less than a right angle. 

Fig. 2 . 


An obtuse angle is greater than a right 
angle. F i g . * 




TRIANGLES. 

ALL THREE-SIDED FIGURES ARE TRIANGLES. 


An equilateral triangle is one whose sides are 
all equal. Fig * 4 - 

A scalene triangle is one whose three sides 
are unequal. Fig# s- 





A right a?igle triangle is one which has a 
right or square angle. Fig - 6 - 


Note. —It is composed of abase perpendicular and hypoihenuse. 
The sum of the three angles of every triangle is 180 degrees; the 
right angle being 90 and the other two 90. 


An isosceles triangle has two of its sides equal. 

Fig. 7. 



The perpendicular is the shortest distance 
from any angle of a triangle to the opposite 
side with which it makes right angles. Fig> 8> 















QUA PBIL ATE HALS. 


11 


QUADRILATERALS. 

ALL FOUR-SIDED FIGURES ARE QUADRILATERALS. 

A parallelogram is any quadrilateral whose opposite 
sides are parallel and equal, 

A square is a figure whose four sides are 
of equal length, and whose angles are right 
angles, 


A rectangle is any right angle parallelogram. 

Fig. io. 


A rhombus has all its sides equal but its 
angles are not right angles. Fig - ”* 


A rhomboid is a figure bounded by 
four sides, the opposite ones being 
equal and parallel, but whose angles 
are not right angles. Fig - l2- 

Note. —The perpendicular height of a rhombus or rhomboid is a 
line drawn from one of the angles to its opposite side. 


Fig. 13- 

A trapezoid is a figure bounded by 
four sides, two^of which are parallel, 
though of different lengths. 

Fig. *4» 


A trapezium is a figure bounded by four 
unequal sides, no two of which are parallel. 





Fig. i5. 

















12 


LAND SURVEYING. 


A diagonal is a line drawn between 
opposite angles. Fie . l6 . 


Figures with more than four sides are called polygons. 
If the sides are equal the figure is called a regular polygon \ 
if unequal, an irregular polygon. 



CIRCLES. 


A circle is the space bounded by a curve 
line, every part of which is equally distant 
from a point within called the centre. 

Fig. 17* 

The circumference of a circle is the curve line which 
bounds it. 



The diameter of a circle is a straight 
line passing through its centre, terminat¬ 
ing at the circumference. Fig l8 



The radius of a circle is the distance 
from the centre to the circumference. 

Fig. 19. 



An arc of a circle is any part of its 
circumference. K . 

Fig. 80. 

A chord is a straight line drawn from 
one end of an arc to the other, and is the 
measure of the arc. 


Fig. 21 . 








CIRCLES. 


ia 


A tangent is a right line which touches 
a curve at one extremity of an arc. Fig . ^ 


The segment of a circle is that portion 
cut off by the chord. Fig 23- 

Platting is representing on paper the lines and angles 
measured on the ground. 

A map of a survey represents the lines which bound the 
surface surveyed and the objects upon it, such as houses, 
hills, rivers, roads, etc., in their true relative positions and 
dimensions. 

A plat oi a survey is a skeleton, or outline map. It is 
a figure similar to a map having all its angles equal and its 
sides proportional. 






Fig- «4- 

























































CHAPTER II—Instruments. 


THE COMPASS. 

The main instrument used in all surveys is the Compass. 
It should be thoroughly studied and understood before any 
field work is attempted. The cut on the preceding page 
represents a plain Surveyor’s Compass with a Vernier plate 
attached. 

A Compass is made on a brass plate, and is composed of 
a compass box, the interior of which is a graduated circle 
divided to degrees and half degrees, and numbered from 
0 at the North and South end to 90 on the right and left. 
At the centre is a small pin on which the magnetic needle 
plays. The length of the needle is a very little less that? 
the diameter of the graduated circle, so that it can.movt 
freely around its centre, within the circle, and its positions 
be noted on the graduated arc. 

At each end of the Compass is a perpendicular brass 
sight fastened to it by thumb screws. In each sight there 
are holes or small apertures and slits. In some Compasses 
this sight is simply a thread or hair drawn vertically through 
the middle ; in others, merely small apertures or slits in 
the brass. These sights are set on the Compass-plate cen¬ 
trally over a line passing through 0 at the North and South 
or N. and S. end of the graduated circle. All these ar¬ 
rangements are intended to enable the line of sight to be 
directed to any desired object with ease and precision. 

A Vernier, which is a movable graduated plate for meas¬ 
uring smaller portions of space than those into which the 
line is actually divided, is attached to most Compasses. It 
consists of a second line or scale, movable by the side of the 



16 


LAND SURVEYING. 


first and divided into equal parts, which are a very little 
shorter or longer, than the parts into which the first line is 
divided. The Vernier is permanently attached to the 
Campass-box, and is moved about the centre by means 
of a thumb screw on the right or left. When the Vernier 
is not used care should be taken that the 0 should coin¬ 
cide precisely with the 0 of the Compass-plate. When a 
needle is well magnetized and the centre nicely pointed 
it will play lively and long. When it ceases to move, by 
giving the staff or compass a light rap it will sometimes 
move slightly and rest a quarter, half, or a whole degree 
from the true point. This is nearly always true when £he 
needle settles quick. It is sure evidence that something is 
out of order. The needle, therefore, should not come to 
a rest very quickly. If it does, it indicates either that it 
is weakly magnetized or that the friction on the pivot is 
great. When it is very sensitive and lively it will be in¬ 
dicated by the number of vibrations it makes in a small 
space before coming to rest. The needle should always 
be raised off the pivot when the instrument is being car¬ 
ried about, that the point may not be dulled and cause 
unnecessary friction. But when the Compass is not in use 
the needle should be free on the centre pin that, by keep¬ 
ing its polarity, the magnetic power will strengthen rather 
than weaken. 

In many Compasses each end of the needle does not 
rest or point at the same degree; care should therefore be 
taken to always read the courses from the same end of the 
needle, which should be the North end. Any Compass is 
liable to this trouble when it is not level. Compasses dif¬ 
fer in their directions because different needles do not 
point alike at the same place. It was well known to the 
celebrated Rittenhouse, who manufactured instruments, 
that his Compasses did not agree, and he was never satis¬ 
fied as to the cause of it. As correct a survey may be 


TIIF, COMPASS. 


17 


taken with one as with another of this class, and we may 
naturally ask the question, which of these varying Com¬ 
passes is correct ? We answer, all are correct. All that 
can be said of them is, that one makes a greater declina¬ 
tion than another, and that which makes the least cannot 
have the preference. To remedy this defect, if it is prop¬ 
erly a defect, the Vernier scale can be used to regulate the 
difference and make all agree on the same meridian. The 
meridian should be established by the motion of the heav¬ 
enly bodies and made permanent by durable monuments. 

All courses are counted North or South so much East or 
West. That is, the angle which a course makes with its 
meridian is written North so much E ist or West, or South 
so much East or West, unless the needle reads 90 degrees; 
in that event the course is either due East or due West. 

The North end of the Compass’ dial is generally indi¬ 
cated by some ornamental drawing or the letter N; the 
opposite end by the letter S; the left hand by E, and the 
right hand by W. Tne latter may seem to be the reverse 
of what it should be, but a little thought will prove its 
correctness. Suppose the North end of the Compass be 
turned due East, the needle reads 90 under or at E, show¬ 
ing that the course is East, and vice versa. Should the 
North end be turned due West, the needle reads 90 at W, 
showing that the course is West. Thus the lettering is 
correct, and is an unerring guide in taking bearings. 

The Compass is generally supported on a single leg, 
called “Jacob’s Staff,” which should be shod with iron 
or steel. A temporary one may be made of any wood at 
the place where it is to be used, thus saving the trouble of 
carrying it from place to place. It is much better, how¬ 
ever, to have one of good durable wood mounted with 
the usual brass ball and socket. It admits of motion in 
any direction, levels the instrument easily, and can be 
tightened or loosened by turning the upper half of the 


18 


LAND SURVEYING. 


hollow piece or case enclosing it, which is screwed on the 
lower half. 



This useful instrument is essentially a Vernier Compass, 
to which is attached a telescope supported by upright 
standards firmly fixed to the movable plate. The teles¬ 


cope can turn completely over so as to take back and fore 
sights—hence the name Transit. The chief advantage of 
the Transit over the Compass in common surveying is the 








THE CHAIN. 


19 


use of the telescope, which enables the Surveyor to prolong 
lines to a greater distance and with more precision than 
with the eye. I will not give an extended description of 
the Transit for the reason that it is seldom used in land 
surveying. It is a heavy instrument supported on a tripod 
which renders it impracticable for common use. Its prin¬ 
cipal use is in railroad surveying. 


THE CHAIN. 



The measur« most commonly used in land surveying is 
a chain 66 feet, 4 rods, long, and is composed of 100 links 
made of wire. Every tenth link is marked by a brass 
tag having one, two, three and four points numbering the 
tens from the hind end of the chain. This chain was 
invented by Mr. Edward Gunter, and is usually called 
“Gunter’s chain.” The length, 66 feet, or 4 rods, was 
chosen because each square chain contains 16 square rods, 
and 10 square chains make one acre. Since each link is 
the hundreth part of the chain, and links therefore deci- 



20 


LAND SURVEYING. 


mal parts, they may be so written, 4 chains and 65 links, 
simply being 4.65 chains, and all calculations in chains 
and links can be easily made by the rules of common deci¬ 
mals in Arithmetic. ‘Each link is 7.92 100 inches long. 
To prevent a very common error of calling ten, forty, or 
twenty, thirty, care should be taken by the Surveyor to see 
that the proper end of the chain is before. That is in¬ 
dicated by the greatest number of points on the brass tags. 
Most all field work is done with a half, or 2 rod, chain, 
which is more convenient than a whole chain. It is com¬ 
posed of 50 links, numbered as above, by the brass tags. 
In taking measurements with the half chain the number 
must be halved to get the correct number of chains, but 
links should not be. 

A chain 50 feet or 100 feet long, each link 12 inches 
long, is frequently used in taking measurements and is very 
convenient to count. It likewise has the brass tags, the 
same as Gunter’s chain. It is very easy to reduce the feet 
to chains and links by simply dividing by 66 and contin¬ 
uing the division to two decimal places for links, which, 
as stated above, are merely hundredths of chain. 

To reduce chains and links to feet multiply by 66 and 
cut off two figures from the right for decimals ; if no links, 
the product of chains by 66 is the number of feet. The 
Author uses a 50 feet chain in surveys, and makes all cal¬ 
culations of area by feet, stating length of lines on plats 
and maps in feet. He prefers this method of measurement 
as it is just as accurate as by chains and links, and much 
more easily used in platting and more readily understood 
or comprehended by the people. When measurements are 
taken in feet the platting should be in feet or by the foot. 


CHAPTER III—How to Chain. 


Chaining is the foundation of all kinds of Surveying. 
Two hands are required to chain, and they should be care¬ 
ful and attentive to their duties. The chain should be 
measured to see that it is correct in length. All lines in 
land surveying must be measured horizontally as if level 
like a plane. A hill thus measured will give the same 
contents as the level base upon which it is supposed to 
stand. Thus in chaining slopes, the chain should be car¬ 
ried level; if going up the slope, the fore chainman puts 
his end of the chain down and the hind chainman raises 
his end of the chain to a level, taking care that the end is 
vertically over the pin or point. And in going down the 
slope, the hind man holds down at the pin and the fore 
man holds up to a level and drops the pin on a perpendic¬ 
ular. This is the only method by which the correct meas¬ 
ure of uneven surfaces is obtained. Eleven pins are re¬ 
quired in chaining—the fore chainman starts with ten, 
leaving one to the hind man. The chain should be tight¬ 
ly stretched every measure, the hind man placing the end 
of the chain against or directly over the pin and calling 
out “stick;” the fore man sticks a pin and calls out 
i “stuck,” when the hind man takes up the pin, and never 
| until that announcement is made, and goes forward to the 
j next pin, and so on. When the fore man gets all the pins 
stuck he should announce “out,” distinctly, when the 
hind man drops the chain and carries up the pins, count¬ 
ing to see that there are ten. 

Both put a small rock or something of the sort in their 
pockets to number the “outs” or tens. The fore man 
now starts off anew with ten pins, as at first, the hind man 




22 


LAND SURVEYING. 




measuring from 


the last pin stuck down. When the ob¬ 
jective point, or end of the line, is reached, get as close 
to it as possible with full chains and carefully count the 


links from the last pin to it. The hind man announces 


the number of pins in his hand, without the last one stuck. 
Then to make up the length of the line count the outs, or 
tens, multiply the number by ten and add the number of 
pins in the hind man’s hand ; this will give the number of 
chains, to which add the links. Of course if the chain 
comes out even, then the hindman is entitled to the last 
pin stuck down. 

Too much care cannot be taken in chaining, especially 
on broken or uneven lands. The very best that can be 
done, the lines of such lands are generally made too long. 
A judicious, experienced Surveyor can form a pretty cor¬ 
rect idea what allowance to make in such cases. It may 
be asked why the chain should be leveled every measure. { 
We answer, in common surveying the earth is considered 
a plane and therefore level acres are what are required. 
And, again, if the length of slopes and undulations be 
taken, the measure is entirely too long and the contents 
would be too much. By a little thought on this subject 
we may readily see that no more houses can stand on a 
hill than would occupy the level base, if the hill were re¬ 
moved. Neither can more trees, corn or other plants 
which grow vertically. 

I have dealt thus at length upon chaining because v I de¬ 


sire to impress upon all Surveyors, and more especially 


upon the young Surveyor, the vast importance of being 
careful and accurate in this branch of the work. Careless 
chaining has caused and does cause most of the troubles 
in land matters, and embarrasses even the best of Survey- 





CHAPTER IV—Field Work. 


COMPASS SURVEYING. 

See that the compass is all right before any work is at¬ 
tempted, then set it at the starting point or corner. Then, 
from the very best evidence at hand, get the bearing of 
the line. It is generally best to walk out on the line to 
look for marks, if an old line, as a better idea of the di¬ 
rection or bearing of the line may thus be obtained, and 
then by setting the compass on the marks a start may be 
made. The Author, in traversing old lines, generally takes 
the compass out on the line to mark?, and sets it, between 
marked trees, if possible, taking a uack sight back on the 
corner or a range pole at the corner. Then, by taking a 
sight forward, walk out on the line farther and examine 
for other evidence or marks. If the compass leads off of 
the marks, the bearing can then be changed and a more 
correct start made. But if no evidence of the old^line 
be discovered the bearing thus taken should be run through 
as a random line, the chainman following as directed be¬ 
fore. Should the objective point or corner be missed the 
true bearing of the line can readily be determined by rule 
on page 38 for random lines. The instrument can then 
be placed on that corner, the true bearing applied and the 
line be correctly run back to the first or starting corner. 
In that case, it would be useless to chain back as the true 
length was obtained by the first measurement. 

As before remarked in this work, the compass is subject 
to local attractions, such as iron ore beds, or ferruginous 
substances, hence, to guard against error from this source, 
it is always safe and proper to take a reverse or back-sight 




24 


LAND SURVEYING. 


from every station. If this and the forw?<d bearing are 
the same, that is, if the needle registers or reads the same 
degree, the work is probably correct, but if they differ 
much both should be taken again. Taking the reverse 
sight on a line is generally a great assistance in producing 
a straight line, as well as a safeguard against local attrac¬ 
tion. 

In farm surveying it frequently happens that the bound¬ 
aries are occupied by fences or borders of shrubbery, so that 
it is difficult to chain or to traverse with the instrument. 
In such cases it becomes necessary to make an offset of 
sufficient distance to clear the obstacles. The offset stops 
short or goes beyond the true line a certain distance, and 
the bearing must be the same as the line and of sufficient 
length to pass or clear the obstacle. 

In making these offsets great care should be taken to 
have the ends at right angles with the line. This can be 
done by the eye, in short distances, but should always be 
done by the compass in long lines. The offset can gene¬ 
rally be measured by the flag-staff or Jacob staff. Offsets 
are not only frequently necessary but very convenient in 
surveys; but the Surveyor should use them with great care 
and judgment. 

The foregoing instructions relative to tracing old lines 
or producing new ones presume them to be straight. Tt 
not unfrequently happens that old lines are crooked, and 
the Surveyor will find that no set bearing or variation will 
traverse them, but he will have to content himself with 
following the old marks, provided always, it is not deter¬ 
mined to produce the line straight from corner to corner. 
In this State (Georgia) the law on old lines is: 




“ Natural landmarks, being less liable to change, and not capa¬ 
ble of counterfeit, shall be the most conclusive evidence; ancient 
or genuine landmarks, such as corner station or marked trees, shall 
control the course and distances called for by the^urvey. If the 




COMPASS SURVEYING. 


25 


corners are established, and the lines not marked, a straight line, 
as required by the plat, shall be run, but an established marked 
line, though crooked , shall not be overruled ; courses and distances 
shall be resorted to in the absence of higher evidence .”—Code of 
Georgia , Section 2387. 

(See, also, chapter on Duties of County Surveyors, page 
87, of this work.) 

After an experience of thirty years in Practical Survey¬ 
ing, the Author finds it impossible to bring old lines down 
to a regular standard of variation or bearing, or adopt any 
rule which may be relied on with certainty for re-estabish- 
ing lost lines or old lines, on account of the irregularities 
of the magnetic needle and the difference between com¬ 
passes and the careless and incorrect manner in which most 
of the former surveys were made. It is a noted fact known 
to ail Surveyors of experience that “the original surveys 
of lands in the older States of the American Union were 
exceedingly deficient in precision. This arose from two 
principal causes—the small value of land at the period of 
these surveys, and the want of skill in the Surveyors. The 
effect at the present day is frequent dissatisfaction and lit¬ 
igation. Lots sometimes contain more acres than they 
were sold for and many times less. Lines are frequently 
longer or shorter than laid down on papers, and those 
which are straight in deeds and on the map are crooked 
on the ground. The recorded surveys of two adjoining 
farms often make one overlap the other, or leave a gore 
between them. The most difficult and delicate duty of 
the Land Surveyor is to run out and establish these old 
boundary lines. In such cases, his first business is to find 
corner stones, or monuments, marked trees, stumps or any 
landmarks. These are his starting point and guide. His 
business is to mark out on the ground the lines given in 
the papers.” 


26 


LAND SURVEYING. 


In districts or sections where the land is laid off in reg¬ 
ular lots, it is easy to recheck it with the compass, starting 
from some well known base line, but in head-right dis¬ 
tricts it is more difficult to prove the accuracy of the work. 
It is best and generally necessary to traverse the lines 
twice or more, noting the variations on each, that true 
lines may be established, even if the employer does not 
see the necessity of being so particular. In surveying wa¬ 
ter lines, branches, creeks or rivers, run with an offset, 
generally keeping on the same side of the stream and as 
nearly as practicable about the same distance from it, not¬ 
ing in the field-notes the distance from each station to it 
so as to draw the shape of the stream on the map. 


CHAPTER V. 


VARIATION OF THE MAGNETIC NEEDLE. 

BY 

PROFESSOR WILLIAMS RUTHERFORD, A. M., 

UNIVERSITY OF GEORGIA. 

All that will be attempted in this article will be to deal 
with facts of science without any attempt to explain them, 
as this is intended simply as a Treatise on Practical Survey¬ 
ing. 

It is known to scientific men that the magnetic needle 
is never absolutely still, but that it moves from East to 
West and back from West to East, making different angles 
with the true meridian, of different places on the earth’s 
surface. If the points of attraction were exactly at the 
poles of the earth there would be no variation, for the 
needle would coincide with every meridian on the earth’s 
surface, in all latitudes. This has long been known not 
to be the case. The points of attraction, whatever be the 
cause, are not at the poles, but are removed several degrees 
from each pole. Hence a magnetic needle located on a 
meridian which does not pass through these points will 
make an angle with this meridian differing in amount ac¬ 
cording as the meridian is near or remote from the one 
that does pass through these points, and differing again 
according to the latitude of the place—in higher latitudes 
the angle being greater than in lower. If these points 
were permanently on the same meridian, while the needle 
would vary more at one place than at another, there would 
be no change in the variation for each place. Instead, 



28 


LAND SURVEYING. 


however, of being permanently on the same meridian they 
revolve around the North and South poles in about six 
hundred and sixty-seven years. So that the magnetic 
needle, being always directed to these points, must follow 
them in their motion around the poles. 

Suppose a needle be placed upon the meridian which 
passes through these points of attraction, it will coincide 
with that meridian, and there will be no variation. If, say 
the point of attraction nearest the North pole were mov¬ 
ing in its orbit around that pole at the rate of one revolu¬ 
tion in six hundred and sixty-seven years, in one-fourth of 
that time, that is, in one hundred and sixty-six years, the 
needle will be at what is called its greatest elongation, or, 
in other words, will make the greatest western variation. 
It will then follow the attracting point around the orbit, 
and begin to move back toward the East. At the end of 
about one hundred and sixty-six years more the point of 
attraction will have arrived at the same meridian upon 
which the needle is placed, and there will the needle again 
coincide with that meridian and there will be no variation. 

Still moving eastward, at the end of about one hundred 
and sixty-six years more it will have attained its greatest 
eastern elongation, and then the needle will mark the great¬ 
est angle of variation eastward. After this, following the 
point of attraction, it will move westward, and in about 
one hundred and sixty-six years more will again arrive at 
coincidence with the meridian upon which it is placed, 
being in precisely the same condition as when it started, 
and will run the same round in another period of six hun¬ 
dred and sixty-seven years. 

With these facts, which have been developed by science, 
it will be seen that the magnetic needle has a constant 
though exceedingly slow motion. The motion is so slow 
that for a year or two the difference in the bearing would 
not be observed when marked by an ordinary compass. 


VARIATION OF THE MAGNETIC NEEDLE. 2.9 

But for a number of years, the difference becomes of vast 
importance to owners of land separated by a straight line, 
if all the landmarks be removed. As already stated, the 
variation is not the same for all localities. It becomes 
important for every Surveyor to first determine the annual 
variation of the needle for his locality or county. The 
best practical method to determine this is to select some 
well marked line in the neighborhood, the date of whose 
survey is accurately known, a? well as the bearing at the 
time of the survey. Place the compass accurately on this 
line, and, after the needle has finally settled, take the bear¬ 
ing. It will be seen that it is not the same as the old bear¬ 
ing. Take the difference. This will be the total variation 
for the period of time which has passed between the time 
of the original survey and the present test. Reduce this 
difference to seconds and divide by the number of years 
which have elapsed since the first survey. This will be the 
annual variation for that locality, in seconds. If more 
than sixty, it will be minutes and seconds. The suiveyor 
should not be content with one such test, for it is found in 
practice very difficult to get the exact bearing from marked 
trees. He should take his compass to another portion of 
the line and make the same careful trial, and if there are 
more than one such well marked line in the county, the 
date of whose survey is accurately known, those should be 
tested in the same careful way. 

After taking several such observations, carefully noting 
the bearing each time, add all the results together and di¬ 
vide by the number of observations, and a mean of aP 
will be thus obtained which may be permanently recorded 
as the true annual variation for that neighborhood or coun¬ 
ty. To illustrate : Suppose the surveyor places his com¬ 
pass upon a line which he knows was surveyed October, 
1840—just forty years ago—and the then bearing reads N. 
J5° 30' W., and finds that the present bearing at the first 


30 


I. A ND SU RYEYING. 


point tested reads N. 14 0 15' W. He goes to a second 
point, and finds that the bearing reads N. 14 0 45' W. He 
adds these two bearings together, making 29 0 . Dividing 
by two, he finds the average bearing to be 14 0 30'. He 
decides that the present true bearing of the line is N. 14 0 
30' W., making a difference between the old and new bear¬ 
ing of exactly one degree, or sixty minutes. The time 
between the two surveys is forty years. Now divide the 
total variation by forty, and the result is one minute and a 
half or 1' 30". This is noted as the annual variation for 
the locality. Remembering this as his annual variation he 
will apply it to every line he runs by an old deed or plat 
which gives the date of survey. If tne time between the 
date on the plat or deed is ten years, then multiplying i' 
30" by ten, the result is fifteen minutes, which is the varia¬ 
tion to be applied in tracing the old line. If twenty years 
have elapsed since the old survey, then multiply 1' 30" by 
twenty, which gives 30' as the variation to be applied. The 
next thing to be done is to properly apply the variation 
when found. 

The variation in all States west of Pennsylvania is East, 
and the North end of the needle is moving westward. 
Hence the total variation is becoming less every year. If 
the bearing is N. 15 0 W., the North end of the needle is 
on the right of the line and moving westward the angle 
is becoming less . In this case the variation must be sub¬ 
tracted. Suppose that the annual variation is T 30", and 
twenty years have elapsed since the old survey. This gives 
30', which must be subtracted from the old bearing, say 
N. 15 0 W., making the present bearing N. 14 0 30' W. 
Running with this bearing the old line will be traced; but 
if the old bearing is N. 15 0 E. the needle is on the left of 
the line, and the north end moving westward will increase 
the bearing by the amount of variation. Hence at the 
expiration of twenty years the 30' variation must be added , 


VARIATION OF THE MAGNETIC NEEDLE. 31 


making present bearing N. 15 0 30' E. This, it will be re¬ 
membered, is simply an illustration. 

As said above, each surveyor should determine the an¬ 
nual variation for his county and apply the rule to that 
variation. There is a simple rule by which it may always 
be determined whether to add or subtract the variation. 
The rule is this : If the end of the needle is on the right 
of the line , subtract. If on the left of the line , add. This 
rule will hold good , whether reading the angle from the 
North or South end of the needle. 

To show the importance of always attending to the va¬ 
riation of the needle a few facts may be stated. 

Suppose that the annual variation for a county be T 30", 
and a surveyor be required to trace an old line two miles 
long between two neighbors, where every mark has been 
obliterated and only one corner is known to be a point on 
the line; and suppose that the original line had been run 
forty years ago, the variation would amount to one degree. 
Now suppose the surveyor, as usual, runs by the old bear¬ 
ings which he finds in the deed or plat, he will leave the 
true line one degree, and in running one mile he will cut 
off about five and a half acres from one tract and give it 
to the other. If the dividing line is two miles, or one 
hundred and sixty chains long, he will cut off 22.4 acres 
from one and give it to the other. 

Again, suppose the old survey had been made eighty 
years ago, then the variation will amount to two degrees, 
and if the surveyor runs by the old bearings, in one mile 
he will cut off ii.n acres from one and give them to the 
other; and if the line be two miles long he will cut off 
45 acres, nearly, from one and give to the other. It will 
be seen at once why it is that so many disputes arise about 
land lines. 

That this trouble may be avoided in future let every 
surveyor determine the annual variation for himself and 


32 


LAND SURVEYING. 


always apply it when practicable, and when he makes a 
plat be careful to put upon it, after the scale, the annual 
variation and date of the survey. Then any subsequent 
Surveyor can, with this plat in hand, trace the old line ac¬ 
curately though every mark except the corner be obliter¬ 
ated. • 





CHAPTER VI. 




PASSING OBSTACLES. 

BY 

PROF. WILLIAMS RUTHERFORD, A.M. 

It often happens that in running a line, obstructions are 
encountered, which cannot be conveniently passed. If it 
be a pond of water, and the chain-bearers are unwilling 
to wade it, or if it be too deep for wading, it becomes 
necessary to adopt some expedient by which it can be 
passed without going directly through it. If a tree, or 
any well-marked object, can be seen in the direct line 
across the pond, note it. Then take the bearing to some 


fig. 25. 



convenient point from which a direct line to the object 
noted can be run without encountering the pond. Measure 


C 


33 





34 


LAND SURVEYING. 


this new bearing, and note both bearing and distance 
accurately. From this new position take bearing to the 
first object noted across the pond, and measure this line 
to noted object. When the field work is to be platted, 
these two last lines must be laid down, and the end of the 
last will be in the direct line across the pond. Connect 
this point with the point where the offset line was taken, 
and apply it to your scale, and thus determine the true 
distance across the pond, which must be added to the 
other measurements of the direct line. 

ILLUSTRATION. 

The line A B (Fig. 25 ) is measured. The bearing from B to D is 
taken, and the line measured. The bearing and distance from D to C 
are taken and measured. When platted, one foot of the dividers is 
placed at C and the other at B, and applied to the scale, and the 
distance counted as are all other distances in the same plat. 

FIRST METHOD. 

If no object can be seen, then a different method must 
be adopted. When the point B is 
reached (Fig. 26), turn at right 
angles to A B until the point D is 
reached, from which the line D E 
parallel to A B will pass the pond. 
Then from E run E C parallel to 
first offset and of the same length. 
The point C is in the direct line, 
and the length of E D must be added 
to A B, making the direct line from 
A to C known. 

To find distance to inaccessible object with chain or rod 
pole alone . 

Let it be required to find the distance across a river to 


fig. 26. 

Parallel to B D. 








PASSING OBSTACLES. 


35 


any object*on the opposite bank, when the person has no 
instrument with which to measure angles, 

SECOND METHOD. 

Let A be the object on the opposite side of a river, and 
it be required to find the distance from B to A. Place 
a man or stake at B, and measure accu¬ 
rately B F in a direct line with A B. Then fig. 27. 
measure F E at right angles from the line 
A F to a convenient distance F E. Then 
standing at E, look towards A, and place 
a man or stake at D in line with A, and 
also in a line B C parallel and equal to F E. 

Then measure D C. There will thus- be 
formed two similar triangles D C E and 
A B D. Their homologous sides can be 
compared thus :DC:CE::BD:AB. It will be seen 
that as we have the length of D C, C E, and B D, we can 
find by the ordinary rule of three the value of A B, the 
distance desired. 



fig. 28. 



WITH A COMPASS AND CHAIN. 

Let A B (Fig. 28) be part of a line of survey in which 
A and B are on opposite sides of a river. From A at right 























36 


LAND SURVEYING. 


angles to A B lay off any convenient distance, as A C, so 
that B may be seen from C; remove the instrument to C, 
and lay off C D at right angles to C B, fixing the point D 
in A B produced, and measure D A. Then square the 
length AC and divide by DA; the quotient will be the 
distance A B, the width of the river. 


CHAPTER VII. 


RANDOM LINES. 

BY 

PROF. WILLIAMS RUTHERFORD, A. M. 

To run a straight line between two corners or points where 
all intermediate marks have bee?i obliterated, and the corners 
cannot be seen the o?ie from the other. 

It frequently happens that a person wishes to sell a piece 
of land to a line running from one point to another which 
cannot be seen, and again it may be desired to run an old 
line between two such corners, when every marked tree or 
other monument has been destroyed and the original bear¬ 
ing lost. Set your compass at one of the corners, and 
direct the sights as nearly as you or some one present may 
guess to be the direction. Note your bearing and measure 
accurately until opposite the other corner or point desired, 
if not exactly in the line run. Then measure the offset to 
the corner. This offset, random line just run, and the true 
line, will form a triangle, and the angle at the starting-point 
will be the angle by which you missed the true bearing. 

There are two practical methods of finding this angle 
without the use of a table of tangents, which the surveyor 
seldom carries with him. 

FIRST METHOD. 

Make this statement: As the length of the line measured 
is to the offset by which you missed the second corner, so 
is 57.3 to the number of degrees and tenths of a degree in 
the required angle. Having reduced the tenths of degrees 
4 37 






38 


LAND SURVEYING. 


to minutes, set your compass at the corner missed, and turn 
your sights until the same angle is indicated by the needle 
with which you ran yo.ur random line. Now looking in 
the line of back-sight, turn your compass towards the 
corner from which you started, until the needle passes 
over the degrees and minutes obtained by the above state¬ 
ment. Note the bearing now indicated by the needle and 
run back to the corner, marking trees or setting stakes. If 
the work has all been accurately done, this will be the true 
line, and take you back to the beginning corner. An illus¬ 
tration will be given to be sure that the student will under¬ 
stand the method. 


jf IfS JSa 


fig. (a.) 

e 8%.ooR« v do m Line 



True -Line 


Suppose A is the point at which you start, and C is the 
second point you wish to reach. Place compass at A, and 

direct along the line A B; 
say that the bearing is N. 
45 0 E., and the distance 
from A to B, opposite C, 
measures 84 chains, and the 
offset from B to C measures 2 chains. 



Then you have 

84 : 2 :: 57.3 : o Q, the arc which measures the angle B A C. 
2 

84 )ii4.6( i°.364 
60 


21.840 The angle is found to be i°2I / ,8. 










RANDOM LINES. 


39 


After calculating thus, set your compass at C, and turn 
the sights until the needle stands at S. 45 ° W. when look¬ 
ing in the direction of A. When the needle is well settled, 
move sights towards A until the needle passes over i° 22'. 
Then read bearing, and this will be the true bearing be¬ 
tween the corners. 

From the above illustration we have the following simple 
rule: 

Multiply the offset by 57.3, and divide by the length of 
the line. Then add or subtract as required. 


SECOND METHOD. 


Run line as in the first method. Double the distance 
(A B) and multiply by 3.14159. The product will be the 
length of the circumference of a circle, whose radius is 
A B. The offset (B C) will be a part of the circumference 
which measures the angle B A C. If the whole circumfer¬ 
ence of the circle be divided by 360, the length of one 
degree will be found. The true length of the offset (B C) 
compared with the measure of one degree will give the 
degrees of the angle B A C. Illustration by the same ex¬ 
ample : 84 chains being the measured distance from A to 
B, the double distance will be 168. This multiplied by 
3.i4i59gives 527.78712. This divided by 360 gives as 
a quotient 1.466. Now divide the offset 2 chains by this 
result, that is 


2 

[.466 


i°.36* 

60 


21C840 


giving the angle BAC i° 2i'.8, precisely the angle ob¬ 
tained by the first method. Having found this angle, pro¬ 
ceed just as directed in the first method. 



CHAPTER VIII. 


KEEPING FIELD-NOTES. 

This is an important branch of the work, and the sur¬ 
veyor must not only be correct, but also exceedingly care¬ 
ful in recording his field-notes, so as to be able to make 
an accurate map. An error here may make it necessary to 
do the entire work or a great portion of it over. A small 
blank book of convenient size for the pocket is provided. 
Enter the date of the survey, what survey it is, for whom 
done, and the names of the chainmen. Then describe the 
beginning corner carefully and fully, set the instrument on 
it as before directed; get the bearing of the line, which is 
entered in the book, together with all objects on the line 
it is desired to note. The line is produced through on 
the bearing noted, and the length measured by the chain- 
men. The length is then entered opposite the bearing, 
and the second corner or station mentioned. Set the com¬ 
pass on this second corner, take and enter the bearing and 
length as before, noting all objects necessary for an accu¬ 
rate map. Continue with every line until the starting- 
point is reached and noted. 

It matters little which way the land is run, whether to 
the right or to the left. But a map looks better with the 
courses and distances taken with the course of the sun— 
that is, with the land on the right. All the rules deduced 
for the one case are equally applicable to the other. To 

40 




KEEPING FIELD-NOTES. 


41 


illustrate the above method of taking and recording the 
field-notes of a survey, it may be well to give an example 

or two. 


FIG. 30. 

KO.-y N.S1S.W eU . p lne 




2 

£ 

Po.-p. 

y 


H. D. Human 

(0 acres* 


S , 87 W. tO chs. 


Cu> 

jn 

& 

«■» 


«Tkp 


August 18, 1880. 

THE “ PICKET SURVEY. ’* 

FOR H. D. HUMAN. 

Tohn Charles, I . 

J ’ s- Chavnmen. 

William Roe, J 

Begin Post Oak, southwest corner of the survey. 

Thence N. 3 W. 10 chs. Red Oak. 

“ N. 87 E. 10 chs. Pine. 

“ S. 3 E. 10 chs. Poplar. 

** S. 87 W. 10 chs. Beginning. 

If the measurements are in feet, the field-notes would 
read : 


Begin at Post Oak, southwest corner of the survey. 

Thence N. 3 W. 660 feet. Red Oak. 

“ N. 87 E. 660 feet. Pine. 

“ S. 3 E. 660 feet. Poplar. 

“ S. 87 W. 660 feet. Beginning. 


The above plan of keeping field-notes is used by the 
Author. It is plain, easy, and simple. Of course, where 
the survey is more complicated, and it is desired to note 

4* 





42 


LAND SURVEYING. 


various objects, such as houses, fields, branches, roads, etc., 
the notes must be fuller and more explicit. Another good 
plan is to make a rough pencil-sketch of the survey by the 
eye, and write down on the lines their bearings, lengths, 
and corners. Upon this sketch it is easy to represent 
branches, houses, fields, and all objects necessary for a full 
and clear map, and also the names of adjoining land- 
owners. I will give a few more examples, which will 
suffice to show and teach the student how to keep his 
field-notes, and from which he can make his maps and 
estimates. * 


FIG. 31. 



THE “S. E. IVEY SURVEY.” 

John Morse, 1 chainmm . 

Jasper Jones, f 

Begin at Rock, southeast corner of lot and corner of lands of Bag- 
well and Jones. 

Thence S. 57 W. 560 feet. Rock.—Morse’s corner. 

“ N. 33 W. 716 feet. Rock.—Lane’s corner. 

“ N. 57 E. 560 feet. P. O. & R.—Bagwell's corner. 

u S. 33 E. 716 feet. Rock.—Beginning. 





KEEPING FIELD-NOTES. 


43 


October 4, 1879. 

THE “BOYD” LOT. 

FOR JOHN C. JARRETT. 

JOHN C. JARRETT, 1 chainmm _ 

B. F. Small, J 

Begin at Rock on Jefferson road, near the Jarrett dwelling. 

Thence N. 84^ W. 1475 ^ eet along said road to Red Oak. 

Thence S. W. 600 feet to White Oak in fork of branches. 
Thence S. 34 E. 562 feet to Gum, the corner of Harmony church 

lot. 

Thence N. 43^ E. 350 feet to Rock, the corner of Harmony church 
lot. 

Thence S. 46^ E. 218 feet to Rock, the corner of Harmony church 
lot. 

Thence N. 43^ E. 1079 feet to Beginning corner. 

David H. Jarrett marked the lines. 

W. P. Mangum, 

T. N. Buffington, C Processioners. 

William R. Cato, j 

To record the above survey on a reverse run: 

Begin at Rock corner on Jefferson road, near the Jarrett dwelling. 
Thence S. 43^^ W. 1079 feet to Rock, corner of Harmony church 

lot. 

Thence N. 46^ W. 218 feet to Rock, corner of Harmony church 
lot. 

Thence S. 43^ W. 350 feet to Gum, corner of Harmony church, 
lot. 

Thence N. 34 W. 562 feet to White Oak, in fork of branches. 
Thence N. 1% E. 600 feet to Red Oak, on Jefferson road. 

Thence S. 84E. 1475 ^ eet along said road to Beginning. 

September 4, 1879. 

FOR J. M. THOMPSON. 

W. A. Dunagan, V/’i • 

V Chainnien. 

George R. Watson, j 

Begin at Willow on west bank of the Oconee River, Hancock’s 
comer. 

Thence N. 70 W. 450 feet to branch, 1240 feet to road, 2000 feet to 
Hickory. 


44 


LAND SURVEYING. 


Thence N. 30 E. 1025 feet to road, 1650 feet to field, 2500 feet t< 















KEEPING FIELD-NOTES. 


45 


This example must suffice to teach the student how to 
run and record water or road lines when either is a boun¬ 
dary line. It is generally best to make a pencil-sketch or 
draft, and note the lines and offsets on all such boundaries. 
When the surveyor runs short chords or lines, it may be 
unnecessary to measure the distance to the stream at the 
various stations or points at which he curves. He can 
keep about the same distance from the stream, and note 
the distance to the larger curves, so that in mapping he 
can show them with sufficient precision. In taking field- 
notes, the surveyor can adopt his own method, and should 
do so as far as possible. In the above instructions the 
Author has given simple methods, easily understood and 
reduced to practice by the student. 






CHAPTER IX. 


PLATTING. 

Platting the work is the nicest part of the duty of a sur¬ 
veyor, and he should not only study the various methods 
well, but also practise them a great deal, that he may be¬ 
come expert in this branch of the work. To be able to 
make a correct and handsome plat or map of his work is a 
strong recommendation to any surveyor. Since the esti¬ 
mates of the area depend entirely upon a correct plat or 
outline of the field-work, it becomes very necessary that 
great care should be exercised in platting. There are 
many methods taught in the extensive works on Surveying 
now extant, but the author will content himself in giving 
two plain practical methods, either of which the student 
will find easily reduced to practice. 


fig. 33. 



The one is with a Protractor, and the other with a Scale 
of Chords. 

It is not necessary to present the student with a minute 

46 





















PLATTING. 47 

description of all the drawing instruments usually found in 
a case, a* he will have them before him, and will readily 
perceive the use of each, or be instructed by his teacher. 

The instruments most commonly used in plain platting 
are the scale, protractor, and dividers or compasses. 

The scale is of boxwood or ivory, generally six inches 
long, divided into inches and subdivision of inches, chains 
and tenths of chains on one side, and on the other a series 
of divisions numbered from o to 90, and marked C or CH. 
This is a scale of chords, and gives the length of the chords 
of any arc for a radius equal in length to the chord of 60 
degrees of the scale. 

THE PROTRACTOR. 

A protractor is made of horn or brass, a semicircle 
divided into degrees and half degrees, numbered in both 
directions from 1 to 180, similar to the face of the com- 


FIG. 34. 



pass. It will be seen from the figure above that it has a 
straight side, the middle being marked by a notch, which 
is also the centre of the semicircle or semicircumference. 

THE DIVIDERS. 

The dividers are made of brass, and consist of two legs 
meeting at and revolving about a common joint or centre. 













48 


LAND SURVEYING. 


The principal use of this instrument is to lay off distances 
or lengths of lines to a certain scale. There are various 


fig. 35. 



other instruments which are useful or handy in making 
plats, but the three mentioned above are the principal 
ones. 

All plats and maps are made from a given meridian, and 
for convenience the top of the plat is considered north. 
A meridian is required for each corner, or angle, in the 
survey, and the angle of each course is set off by the di¬ 
viders from the scale of chords, or protractor, and the 
length of each line by a scale of equal parts. These me¬ 
ridians, or parallels, may be set off by the dividers or a 
parallel rule; but the easiest, and perhaps the most accu¬ 
rate, plan is by means of a T square. It is simply a ruler 
let into a thicker piece of wood or stock at right angles to 
it. The stock is of uniform width and straight, so that 
either the side next the ruler or the opposite side may be 
used in setting off parallels. In using the T square, it is 
necessary to have a straight base line, as the edge of the 
paper, table, or mapping-board, or a line drawn at right 
angles to the meridian on the paper upon which the plat 
is to be made. It is then convenient to run the T square 
along it to different stations, and set off the parallels. If 
a straight-edged mapping-board is not convenient, a strip 
of plank with a straight edge may be fastened to any table 
with a smooth surface, along which the stock of the T 
square may be slipped to the different stations or angles. 


PLATTING. 


49 


Every surveyor should prepare a rectangular mapping- 
board or table sufficiently large for any size map, with 
each end at right angles with the sides. Then procure a 
correct T square with stem long enough to span the table, 
and he will find his platting easy, rapid, and correct. This 
is the method used by the Author. 

TO PLAT WITH THE PROTRACTOR. 

The paper is fastened to the table, and with the T square 
draw a meridian, having reference to the size of the plat 
and the side you desire to commence, so the plat will not 
run off the paper. At some convenient place on this me¬ 
ridian line make a dot, and enclose it with a small circle 
with the pencil, and from this as the starting corner, or 
first station, lay Off the bearing of the first line with the 
protractor. With the dividers set off the length of the 
first line to any desired scale, and mark the end with a 
small dot, enclosing as before to show that it is a station. 
Through or immediately over this dot or mark draw another 
meridian, and with the protractor lay off the angle of the 
second line and set off the length, designating the station 
each time as above directed. Proceed with the remaining 
courses in the same manner, and when the last course and 
distance are platted, they should end precisely at the start¬ 
ing point, as the survey did. Should the plat not close or 
come together, some error exists either in the field-work 
or in the platting. It will generally be discovered where 
the error is by replatting carefully, or by making a reverse 
plat; that is, by platting in opposite direction to the one 
first used, reversing the courses. Sometimes it is necessary 
to plat 'from some other corner or station, in order to de¬ 
tect the error, which may be either in the bearing or in 
some measurement, or in both. The surveyor will never 
realize the importance of strict accuracy in the field-work 
until he attempts to plat his work, and after several efforts 
5 D 


50 


LAND SURVEYING. 


utterly fails to make it close. The trouble is oftener in 
the measurements than anywhere else. The most careful 
chainmen will sometimes make mistakes in the outs, and 
report a line five chains longer or shorter than it is. Hence 
the trouble in platting the work. 

Since it is not at all likely that errors have been made 
on all the lines, and that all the lines and bearings should 
be changed in the same proportion, it follows that no gen¬ 
eral rule can be made to fit each particular case. The sur¬ 
veyor having a full knowledge of the conditions under 
which the survey was made can readily tell what particular 
line is most likely to be wrong. He can then plat all the 
other lines and close on that one, when the error may be 
detected and the plat closed. In all cases where the plat 
does not close by a considerable discrepancy, a resurvey 
should be made. 


TO CLOSE THE PLAT. 

If it be assumed that the inaccuracy is to be distributed 
among all the lines in proportion to their length, then the 
following rule applies: Multiply the discrepancy by the 
length of the first line, and divide by the sum of all the 
lines. The quotient will give the distance the second 
corner or station is to be in or out. Then multiply the 
discrepancy by the sum of the first and second lines, and 
divide the product by the same sum of all the sides, and 
the quotient will show the distance to move the third 
station. So on for any line desired. Add the line to all 
the preceding lines, and multiply the sum by the discrep¬ 
ancy, and divide as before; the quotient will show how 
much the corner is to be moved in or out. 

TO PLAT WITH A SCALE OF CHORDS. 

Draw an indefinite line, as from i to 2, and from the 
scale of chords open the dividers from zero, or o, to 60, 


PLATTING. 


51 


set one leg at i, and describe the arc A B of sufficient 
length for the angle. Take the distance, 35, on the same 
scale of chords, set one leg 
of the dividers at A, and FIG * 36- 

make the point B on the arc 
A B, and with the ruler de¬ 
scribe the line from 1 to 3. 

The angle of 35 degrees is 
set off from the meridian 1 
to 2. 

If it be desired to produce 
another line from B, draw a 
meridian through B parallel 
to 1 and 2 ; then with the 
dividers describe the arc of 
60 degrees, as before, either 
north or south as required, 
and on the east or west side 
of the meridian, and then 
set off the degrees desired, making a station on the arc. 
Draw a line from B through this station, and the desired 
angle is set off from B. If the student desires to produce 
a plat by this method, he must define the length of each 
line by the dividers to any scale he may choose. Proceed 
as above described with each succeeding line to the be¬ 
ginning corner. One example, with minute instructions, 
will suffice to teach this lesson by both methods of 
platting. 

WITH THE SCALE OF CHORDS. 



Draw the meridian marked N and S. From the scale 
of chords open the dividers to 60 degrees, and from 1 de¬ 
scribe an arc on the east side of the meridian N S from the 
north end, since the bearing is to the northeast. Now 
open the dividers to 18, and set off the bearing of line 1 
and 2, and with the ruler draw the line long enough to get 





52 


LAND SURVEYING. 


the net length, 20 chains. Take a common square, or any 
rule with inches, from which take the length of the line to 


FIG. 3 7 . 



Scale —10 chains to i inch. 


any scale, as 10 or 20 chains to the inch, and designate j 
the end by a station mark O at 2. Through the station 2 
draw a parallel meridian, and on the north end and east 1 
side draw the arc of 60 degrees, setting one leg of the 1 
dividers at 2. Then from your scale get 8 chains, and ] 
mark station 3. Another parallel is drawn, and the arc | 
60 degrees described on the southeast side from 3. The \ 
angle of 12 degrees is defined on this arc, and the line 3 
to 4 drawn. The length, 17 chains, is taken from the j 
scale, and station 4 made. Through 4 the last parallel is j 
drawn, and the arc of 60 degrees on the southwest side, 
since the direction of the line is southwest. The angle, { 
77 degrees, set off and the line from 4 through 1 drawn. 








PLATTING. 


53 


Now get 18 chains from the scale, and the plat is closed 
at i, the beginning corner. 

To make the same plat with the protractor. 

With the T square draw the meridian N S, and make a 
station O on it. Lay the protractor on the meridian, on 
the east side, so that the notch on the straight side will be 
at i. With some sharp-pointed instrument make a dot at 
18 degrees, and from i draw the first line through this dot 
or point. Take 20 chains from the scale with the dividers 
and make station 2. Bring the T square up to 2 and 
draw the second parallel, and lay the protractor at 2 on 
the east side, and mark the point at 78 degrees from the 
north side. Draw this line from 2 and set off 8 chains, 
and mark 3. Move up the T square to 3 and draw the 
third parallel. With the protractor at 3, as before directed, 
make a point at 12 degrees from the south side, as the 
course is to the southeast. Draw the line from 3 over this 
point and set off 17 chains, and mark 4. Slide the T 
square up to 4 and draw the last parallel. Now lay the 
protractor on the west side of it, with notch at 4. Desig¬ 
nate 77 degrees by a small dot from the south side, and 
make a line from 4 over 1. Get 18 chains with the di¬ 
viders, the length from 4 to 1, and the plat is finished. 

As before remarked, this is the most rapid, and at the 
same time the most accurate, method of platting, and is 
the one used by the Author. 

5 * 


CHAPTER X. 


CALCULATING THE AREA. 

The principles taught in this chapter are purely arith¬ 
metical, and the Author presumes the student is well posted ; 
on common arithmetic before he attempts the study of 
surveying. It is true that the rules for calculating the area . 
of surfaces are based upon geometry and trigonometry, yet 
they may be applied, as we shall do in this work, arith¬ 
metically ; so when the student learns these principles i 
from his arithmetic, he can apply them in his surveying. 
Since getting the area of almost any shaped plat is simply 
calculating so many squares, rectangles, triangles, circles, 1 
or parts of circles, it follows that the principles applicable '• 
to these figures are as easily applied in one place as another, 
in one study as another, and are the same wherever found. 

Area is the contents of the surface expressed in square ] 
inches, feet, yards, rods, chains, acres, or miles. 

The acre is the common unit of measure for land, and \ 
is equal to a rectangle io chains long and i chain wide, 
or 160 rods long and i rod wide, or 4840 yards long and ; 
1 yard wide, or 43,560 feet long and 1 foot wide. A rood 
is one-quarter of an acre, and contains 40 square rods. A 
rod is called a perch. 

Land is generally measured in acres. The fractions of 
an acre may be expressed in roods and rods, but the most 
convenient way of expressing them is in tenths . 


54 





CALCULATING THE AREA. 


55 


If the student will procure a copy of Caldwell’s Arith¬ 
metic, and carefully study the first fourteen pages under 
the head of Mensuration, page 132, he will find it remark¬ 
ably easy to master this chapter of his surveying. The 
principles there taught and the figures used are the same 
we shall employ here. We shall need only a few additional 
figures and instructions. 

To fiiid the area of a square , rectangle , rho?nbus , and 
rhomboid. 


FIG. 38. 

FIG. 39. 




FIG. 4O. 

FIG. 41. 

I 

7 i ~7I 

/ 

LJ 

RULE. 


Multiply the length by the perpendicular distance be¬ 
tween the opposite sides, or the base by the altitude. 

1. A field is 22 chains square. How many square chains 

in the area ? Ans. 484 square chains. 

2. A field is 14 chains long and 8 chains wide. What 

is the area ? Ans. 112 square chains. 

3. A rhomboid is 31 rods long and 26 rods across. What 

is the area? Ans. 806 square rods. 

4. What is the area of a rhombus 30 rods long and per¬ 
pendicular distance 28 rods? Ans. 5.2 acres. 








56 


LAND SURVEYING. 


5. A field, 534 yards long and 438 yards wide, has what 

area? Ans. 233,892 square yards. 

6. A cotton field is 90 yards long and 85 yards wide. 
How many square yards in the field ? 

Ans. 7650 square yards. 

To reduce such questions to acres, divide by the number 
of each measure in one acre; the quotient will give the 
acres, and by annexing one cipher to the remainder and 
continuing the division, we have tenths . Thus, in ques¬ 
tion 5 above, we divide 233,892 square yards by 4840, the 
number of square yards in one acre. The quotient is 48 
acres and three-tenths, with a small remainder. 

Ans. 48.3 acres. 

So in question 3, divide 806 by 160, the number of 
square rods in one acre. Ans. 5 acres. 

I will give the common table of 


SQUARE MEASURE. 


144 

square inches make 

1 square foot, sq. ft. 

9 

square feet 

a 

1 square yard, sq. yd. 

3°X S( l uare yards 

a 

1 square rod, sq. rd. 

40 

square rods 

a 

I square rood, R. 

4 

square roods 

it 

1 square acre, A. 

4840 

square yards 

it 

1 acre. 

160 

square rods 

tt 

1 acre. 

10 

square chains 

ft 

1 acre. 

43,560 

square feet 

it 

1 acre. 

640 

acres 

tt 

1 square mile. 


Note.—F or practical exercise, 70 yards square may be considered j 
an acre, though not strictly correct. As, for example, where land is 
stepped off instead of being measured. 


By the above table the contents of land are calculated. 






CALCULATING THE AREA, 


57 


To find the area of a trapezoid. 


fig. 42. 



RULE. 

Multiply half the sum of the parallel sides by the alti¬ 
tude, and the product is the area.—( Caldwell's Arithmetic , 
P- I 39 -) 

1. A farm is 40 chains on one side, the opposite side 34 
chains, and 22 chains across. What is the area? 

40 -f 34 = 74 2 = 37 X 22 = 814 sq. ch. 

2. What are the contents, when the parallel sides are 800 
yards and 500 yards and the distance across 700 yards ? 

Ans. 94 -f A. 

3. Two sides of a trapezoid are 280 feet and 234 feet, 

and the altitude or distance across is 185 feet. What is 
the area? Ans. 47,545 S T ft- 

To get the area of a triangle. 

fig. 43. 


C 



RULE. 

Multiply the base by the altitude and half the product, 
or multiply the base by half the* altitude.— {Caldwells 
Arithmetic , p. 140*) 








58 


LAND SURVEYING. 


1. A triangle has a base of 40 chains and altitude 15 

chains ? What is the area ? Ans. 300 sq. chs. 

To reduce the 300 chains to acres, divide by 10, the 
number of square chains in an acre. Ans. 30 A. 

2. What is the area of a triangle with base of 140 rods 

and altitude of 90 rods ? Ans. 6300 sq. rds. 

Divide the 6300 by 160, and we have 39.3 A. 

3. A field of triangular shape has a base of 1500 feet 
and an altitude of 400 feet. What is the area? 

Ans. 300,000 sq. ft. = 6.8 A. 

4. What is the area of a triangle whose base is 24 chains, 
14 links, and altitude 13 chains, 84 links? 

Ans. 16.7 A. 

By triangles most of land is calculated. The plat is 
divided into triangles by diagonal lines drawn from oppo¬ 
site corners, or from some point to opposite angles, so as 
not to intersect each other, and the several triangles thus 
formed calculated by the rule above given, the sum of 
which will be the area of the whole figure or plat. The 
correctness of this method depends upon the accuracy of 
the plat and on its scale, which should be as large as pos¬ 
sible. A little practice will suggest the best way to draw 
the diagonals. These should be drawn so as to form as 
few triangles as possible. 

To find ihe area of a trapezium. 

RULE. 

Divide the figure into two triangles by a diagonal drawn 
from two opposite angles. Find the area of each triangle 
and add them together:the sum will be the area. 

A very gross error is often committed as to a trapezium 


CALCULATING THU AREA. 


59 


by taking the average or half sum of the two opposite 
sides and multiplying them together for the area. That 

FIG. 44. 



assumes the trapezium to be equivalent to a rectangle, with 
these averages for sides. 


To find the area of a figure having more than four sides. 


FIG. 45. 


D 



Scale —8 chains to 1 inch. 


RULE. 

Divide the plat or figure into triangles by diagonals ; find 
the area of each of the triangles, and add them together; 
this sum will be the area of the whole plat. 







GO 


LAND SURVEYING. 


This is the method most commonly used by surveyors | 
for calculating the area of their plats. It is easy, simple, 
and practical; but, like every other department of the 
work, great care should be exercised in the use of the 
scale in determining the length of lines, diagonals, and 
altitudes. A slight excess or deficiency in the length of 
either will make an error in the area, and, indeed, may be 
very fatal to the work. The careless use of the scale and 
dividers, with the difference in scales, make the main dif¬ 
ference in results by different surveyors. Hence, two sur¬ 
veyors will run the same piece of land, plat and estimate 
it, and the results will differ slightly. 

Take figure on page 59, above, and apply the rule. 

There are three triangles, ABF, B C F, and C D E. 
The first, ABF, has a base of 20 chains and 40 links and 
an altitude of 8 chains and 10 links. 

20.40 x 8.10 -r- 2 — 82.62. 

The second, B C F, has a base line of 21 chains and an 
altitude of 10 chains and 40 links. 

21 X IO.40 2 = log. 2Q. 

The third, C D E, has a base of 14 chains, altitude 8.50. 

14 x 8.50 -T- 2 = 59.50. 

Add all these several areas together, and we have 

82.62 

109.20 

59 - 5 ° 

25i*3 2 

251 chains and 32 links. 

Reduce to acres by dividing by 10. Ans. 25.1 A. 

This example fully represents the method of calculating 
the area of any plat having many sides and angles. It is 



CALCULATING THE AREA. 


61 


always best, however, to divide the plat into triangles from 
some other angles, and estimate the area again; then, by 
adding the two results together and halving, get the true 
area. 


To find the area of a triangle when the 
side is hnown. 


fig. 46. 


length of each 



49 


RULE. 

Add the three sides together and half the sum. From 
this half sum subtract each side. Then multiply the half 
sum and three remainders together, and extract the square 
root of the product, and the result will be the area. 


Take figure above. 

The sum of the three sides is 50, half of it 25. From 
25 subtract each side, and 6, 9, and 10 are the remainders. 
Multiply 25 by these numbers, and the product is 13,500, 
the square root of which is 116, the area. 

1. The sides of a triangular farm are 40, 60, and 74 
chains. What is the area ? Ans. 119.8 A. 


To get the area of several offsets having a straight base 
line. 

RULE. 

Add the first and last lines, or two outside lines, and take 
half the sum. To this half sum add all the other lines, 
6 





62 


LAND SURVEYING, 


and multiply the sum by one of the equal distances between 
the offsets, or divide the sum by the number of offsets, less 

fig. 47. 



one, and multiply this quotient by the whole length of the 
base line. 

Take figure above, and apply both methods. 

Add 4 and 6, the two outside lines, and half it gives 5. 
To 5 add 3, 4, 5, 6, 4, 5, and 4 gives 36. 

It will be observed that there are 8 spaces between off¬ 
sets; the base line 16 is divided by 8 = 2. Now multiply 
36 by 2, and we have 72 chains, or 7.2 A. 

By the second method divide the 36 by 8, the quotient 
4A shows the average width of the rectangle, whose length 
is 16 chains. Multiply 16 by 4I, and'we have the same i 
result as above. 

The base line of an irregular field is 44 chains, and its ‘ 
breadths at five equidistant points are 8, 10, 9, 14, and 
20 chains. What is the area? 

Ans. 517 chains = 51.7 A. 

CIRCLES. 

To find the area of a piece of land in the form of a 
circle. 

RULE. 

Square the diameter and multiply the square by .7854, 
and point off four figures from the right, or multiply the 
square of the diameter by 11 and divide by 14.—( Cald¬ 
well's Arithmetic , page 143.) 











CALCULATING THE AKEA. 


63 


The diameter is squared to give the area of a square 
figure of the same size, and, as the area of a circle is less 
than it, we multiply the area of the square (the square of 
the diameter) by .7854, which deducts .2146 for the cor¬ 
ners of the square, and leaves the area of the circle.— 
( Caldwell's Arithmetic , page 143.) 



1. A circular farm is 70 chains in diameter. How many 


acres in it ? 


•7854 

4900 

7068600 

3 T 4i6 

10)3848.4600 
384.8 A. 


Ans. 384.8 A. 
70 
7 o 
4900 
11 


H)539oo 

385-0 


The student will observe a slight difference in the results 
by the two methods. Quite as large a class of mathema¬ 
ticians use as use .7854. The Author prefers the use of 
but leaves the student to choose for himself. 

2. A circular piece of woods is 40 rods in diameter. 

How many acres? Ans. 7! A. 

3. A tract of land is 1 mile in diameter. How many 

acres does it contain? Ans. 502 + A. 










64 


LAND SURVEYING. 


The area being given, to find the diameter. 

RULE. 

Divide the area by .7854, or and the quotient will be 
the square of the diameter. Then extract the square root 
of that number, and you have the diameter. 

Since the area of a circle is obtained by squaring the 
diameter and multiplying it by .7854, it follows, to reverse 
the operation, divide the area by .7854 and extract the 
square root, we have the diameter.— {Caldwell's Arithmetic, 
page 125, question 7.) 

1. I have a circular meadow containing 2464 square 

yards. What is the diameter? Ans. 56 yards. 

.7854)2464.0000(^/31.37 

23562 

10780 

7354 

29260 

235 62 

56980 

54978 

2002 

2. What is the diameter of a circular tract of land whose 

area is 5544 square rods? Ans. 84 rods. 

3. The area of a circular tract of land is 314 acres. 

What is the diameter in rods? Ans. 80 rods. 

To find the area of an ellipse. 


RULE. 

Multiply the two diameters together, and that product 
by .7854. 






CALCULATING THE AREA. 


65 


FIG. 49. 





J> 


1. What is the area of 

an elliptical piece of ground 

whose transverse axis is 8 

chains and the conjugate axis 

4 chains ? 

Ans. 2.5 A. 

8 

•7854 

4 

32 

32 

15708 


23562 


10)25.1328 

2 -5 

2. An elliptical farm is 140 rods one way and 72 rods 
the other. How many acres? Ans. 492- A. 

To estimate land by stepping its lines. 

It is assumed that a man can step a yard at a step, and 
that 70 steps square is 1 acre. It is therefore very con¬ 
venient for farmers to estimate their fields by stepping. 
But while it is very useful to the farmer, it is only an 
approximation. Any of the figures given in the preceding 
pages may be roughly estimated by steps as directed for 
measurements, remembering to divide by 7° twice. 

For example, for square or oblong fields step the side 
and end, multiply the two numbers together, and divide 
by 70 twice, and the result will be acres. 

1. A farmer has a cotton field 210 steps long and 150 
steps wide. How many acres ? Ans. 6f A. 

6* E 








66 


LAND SURVEYING. 


210 

* 5 ° 

10500 

210 

70)31500 
70 ) 450 

6 f 

2. A corn patch is 140 steps square. How many acres? 

Ans. 4 A. 

3. A piece of land is stepped off 280 steps one way and 
260 steps the other ? How many acres ? 


Ans. 14-f- A. 







CHAPTER XI. 


DIVIDING LANDS. 

The surveyor is required to lay off land into so many 
different shapes and proportions, it'is difficult to give a 
rule or rules applicable to all cases. The business of 
dividing land must therefore be left in a great measure to 
the skill and judgment of the surveyor, who, if he is posted 
on trigonometry sufficiently to understand getting the area 
of different shaped figures, will not find it difficult, after a 
little practice, to divide up lands as he shall be required. 
It is generally best to have an accurate plat of the land 
before him, so he can see how dividing lines are to be 
drawn to cut off the portion desired. It is always neces¬ 
sary to know the length of bounding lines so as to make 
the proper calculations of the desired lines, knowing the 
area wanted. Only a few rules and examples will be given 
for the general instruction of the student. 

PROBLEM I. 

A SQUARE. 

To lay off a square. 

RULE. 

Reduce the area to chains, rods, or feet, extract the 
square root, and the result will be the length of one side. 
Then proceed with the compass and chain to produce the 
square on the land from the base line and starting corner. 

67 



G8 


LAND SURVEYING. 


1. What is the length in chains of a side of a 40 acre 

field ? Ans. 20 chs. 

40 

10 

v/400(20 chains 
4 

00 

2. It is desired to lay off 60 acres in a square; what is 

the length of a side in rods? Ans. 98 rds., nearly. 

3. A piece of land in a square contains 15 acres. How 

long is each side in feet? Ans. 808.3 ft. 


PROBLEM II. 


A RECTANGLE. 

Having one side and the given area , to find the other side. 
RULE. 

Reduce the given area to the same denomination of the 
given side, and divide that number by the length of the 
given side. Then trace the rectangle on the ground. 


1. A tract of land is 30 chains square; it is desired to 
cut off 45 acres across one side. How long is the other 
side? Ans. 15 chains. 


45 

10 

3 °) 45 ° 

i5 


FIG. 50. 


D 

P 

Cx 

© 

A 


4-5 


30 


C 

O 

B 


To produce it with a compass, measure from D, 15 chains, 
to P; then run the line P O parallel to D C, and 45 acres 
are cut off. 





DIVIDING LANDS. 


69 


2. A base line is 968 feet long, and 8 acres are to be 

laid off in a rectangle. How far down the side will be 
required ? Ans. 360 feet. 

3. A field is no yards long, and contains one-half an 

acre. How wide is it? Ans. 22 yds. 

PROBLEM III. 

A TRIANGLE. 

To cut off a given number of acres by a line from any 
angle of a triangle. 

Get the length of the side opposite the angle from which 
the dividing line is to be drawn. 


RULE. 

Multiply the base line by the number of acres to be cut 
off, and divide by the whole area of the triangle; the 
quotient will be the length to be laid on the base. 

FIG. 51. 


d 



1. The triangle, Fig. 51, contains 24 acres. It is re¬ 
quired to cut off 9 acres from B. How far on the base 
line A B, which is 40 chains long, must be measured ? 

Ans. 15 chains. 

40 

9 

24)360 

15. chains. 




70 


LAND SURVEYING. 


Now measure 15 chains from B to D, and produce the 
line to C, and the triangle BCD contains 9 acres. 

PROBLEM IV. 

To lay off a triangle to contain a given number of acres 
from a certain base. 

* RULE. 

Double the area required, reduce it to the same denomi¬ 
nation as the base, and divide by the base. Or, which is 
the same, divide the area by half the base or half the per¬ 
pendicular. 

The student will perceive, since a triangle is half a square, 
the base or perpendicular must be as long again to embrace 
the same amount of area. 



^0 Chs* 


1. Lay off a triangle to contain 60 acres on a base of 
40 chains. 

60 

10 

40 -r- 2 = 20)600 

30 


FIG. 53 . 



4QCh$. 







DIVIDING LANDS. 


71 


To lay this triangle with a compass and chain, produce 
the base, 40 chains, from A to B, and at right angles, or 
as required, produce the altitude, 30 chains, and by run¬ 
ning a line from C to A (Fig. 53), or the two lines, A C 
and C B, in Fig. 52, the triangle is complete. 

2. It is desired to produce a triangle containing 35 acres 
on a base of 2635 feet. What is the altitude? 

Ans. 1157 feet. 

Again, it may be required to cut off a certain number 
of acres from a given triangle by a line 
parallel to the base. 

Let ABC be a triangle containing 50 
acres, and the surveyor is required to run 
a line parallel to B C, which will cut off 
one-half of the area, or 25 acres, leaving 25 
in the triangle A E F. Square the side A B 
and multiply by 25, and divide by 50, and 
this will give the square of A E. Extract 
the square root of this result, and it will 
give the length of A E. Measure from A 
to E a distance equal to this, and run E F 
with the same bearing as B C. Then E F C B will contain 
25 acres. 

RULE. 

Multiply the area to be left out (A E F) by the square of 
either one of the sides which meet the side to which it is 
desired to run parallel, and divide by the whole area; then 
extract the square root of the result. This gives the dis¬ 
tance to be measured on the side whose square was taken. 
This distance, measured from the vertex of the triangle or 
(angle opposite the side to which it is desired to run par¬ 
allel) on the side squared, will mark the point from which 
a line with the same bearing as the base will cut off the 
amount to be left out in the triangle above, leaving the 




72 


LAND SURVEYING. 


desired area between that line and the base. To illus¬ 
trate : 

Suppose the triangle contains ioo acres, and it is re¬ 
quired to cut off or 33^ acres, next to the base. Then 
there will be left 66§ acres in the triangle. This last area 
is what must be multiplied by the square of one of the 
sides. It makes no difference what be the part desired to 
be cut off, the same principle applies. If ^ of the area is 
to be cut off, then ^ will be left in the triangle, and this is 
what must be multiplied by the square of one of the sides 
of the whole triangle and divided by the whole area, in 
order to get the square of the distance from the vertex to 
the point from which the parallel line must be run. 

A great many examples and problems might be given 
under the head of dividing lands, but it is thought those 
given are entirely sufficient, especially since it is more the 
province of practical surveying to trace lines and lay out 
the land after the shape and area have been determined 
than to solve questions. 



CHAPTER XII. 


SURVEYING BY TANGENTS. 

BY 

PROF. WILLIAMS RUTHERFORD, A.M. 

The surveyor is sometimes required to determine the 
exact amount of cleared land on a plantation. In some 
fields are frequently found rocky knolls, ponds, or marshy 
ground, which are unfit for cultivation, and therefore left 
uncleared. To survey all such places separately and de¬ 
duct them from the field would require a great deal of 
labor and time. The following method has been adopted, 
which saves a great deal of time, and therefore expense, to 
the owner of the land. 

While running around the field, whenever the spot to 
be left out can be clearly seen, note the distance to the 
point of observation and take two bearings , one to the 
extreme right and the other to the extreme left, of the spot 
which it is desired to exclude from the survey. At several 
points on each line around the field take the same observa¬ 
tions, being careful to note the object or objects by their 
numbers (as there may be several in the field), as well as 
the distance to each point of observation and the bearing 
of the two tangent lines. When the field has been run 
around and is to be platted, first lay down the outside lines 
as though none of its area was to be excluded. Then 
with your scale lay off the bearings from each station, 
7 73 





74 


LAND SURVEYING. 


and draw dotted lines through the entire field. These 


tangent lines will intersect each other on the edge of the 
pond or knoll, and will mark it out in the right placej 
The area can be estimated and deducted from the whole 


area included by the outside lines. 


fig. 55. 


Station 4 


5 Station 



Station 2 


Station 1 


Let A B C D E be a field in which there is a marsh or 
pond, abodefg , which it is desired to exclude or leave. 
out from the area of the field, in order to get the exactl 
amount of cleared land. Measure from A to station 1. 
Then take two bearings to edge of pond or marsh, 1 a and 

1 /. Measure on to station 2 and take two more bearings,! 

2 g and 2 e. Take the whole length of AB as usual. 1 
Measure from B to station 3 and take two bearings, 3/i 
and 3 d. Then measure to station 4 and take two other! 


■ 







DIVIDING LANDS. 


75 


bearings, 4 e and 4 c. Finish the whole line B C. From 
C measure to station 5 and take two bearings, 5 d and 
5 b. If these bearings will not enclose the pond as ac¬ 
curately as desired, continue to take other bearings from 
points on lines D E and E A. Where these tangent lines 
cross each other at a b c d e fg, make dots and calculate 
area enclosed by figure thus marked out. It will be seen 
that no measurements are necessary with the chain, and 
the only time lost is the time it may require to take the 
bearings from each station and record them. 





CHAPTER XIII. 


ALTITUDES AND HEIGHTS. 

Taking the Altitudes or Heights of Objects with¬ 
out Instruments for taking Angles. 

To find the height of a tree or other object which casts a 
shadow on a clear day. • 


Drive a stake perpendicular to the level ground, measure 
its shadow and the shadow of the tree or other object.* 
The length of the shadow of the stake is to its length as 
the length of the shadow of the tree is to the height of 
the tree. 

RULE. 


Multiply length of stake by length of shadow of tree, 
and divide by length of stake; the quotient will be the 
height of tree. 


If the sun is not shining so as to cast a shadow, then 
this method may be adopted: Drive a stake about seven 
or eight feet high, so that the observation can be more 
easily made. Tack a lath with a shingle nail to stake a 
little above your head, so that you will have half the lath 
on each side of the stake ; point this one to the top of the 
object. Nail another lath below the first, so that when the 
two ends next to your eye are brought together, it will be 
directed to the foot of the object. Measure the distance 
between the two nails and the distance from your eye 

76 






ALTITUDES AND HEIGHTS. 


77 


(where the two laths cross) along the lower lath to the 
upright stake; also, the distance from the eye to the ob¬ 
ject. Then the distance from the eye to the stake is to 
the distance between the nails as the distance to the object 
is to the height of object. 


fig. 56. 



ILLUSTRATION OF TAKING HEIGHTS OF TREES OR OTHER 
OBJECTS. 

Let B C be the stake stuck at right angles to the level 
ground. Let E F and E G be two ordinary laths nailed 
to stake B C at points B and A. Let the lath E F be 
directed to top , and lath E G to bottom of the tree. Meas¬ 
ure E A and B A and E R 

Then E A : B A : : E R : O R. 

RULE. 

Multiply the distance from the eye to the foot of the 
object by the distance between the nails y and divide by the 
distance from the eye to the bottom nail; the quotient will 
be the height of the tree. All the measurements must be 
taken in inches , and then the final result reduced to feet. 

This chapter, while it perhaps illustrates no principle of 
surveying, is inserted for the practical benefit of the student 
7 * 





78 


LAND SURVEYING. 


and reader. With it the surveying is closed, and the 
author pleads that the rules, methods, and instructions are 
purely practical, and intended to form a hand-book on sur -1 
veying that may be mastered in a few weeks by the student 
who is posted in common arithmetic. 

It is the book that should follow Caldwell’s Practical 
Arithmetic in the schools or out of them, and the student 
will find both simple, plain, and easy, and the shortest 
method ever published. 

In the Appendix, which follows, are some valuable mat¬ 
ters, and should be carefully perused by all into whose 
hands this book falls. For the first time the reason why 
the magnetic needle stands north is published. It has 
always been a hidden mystery, but is now explained by 
that wonderful scientist, Dr. Means, of Oxford, Georgia. * 
This chapter alone is worth the price of the book. 

While the laws given in the Appendix relative to county 
surveyors are Georgia laws, the same principles bear on 
the duties of legal surveyors throughout the country, and 
are similar in all the States. The “ Texas Land Survey¬ 
ing,” from a skilful Texas surveyor, is richly worth a dozen 
books. 



TERRESTRIAL MAGNETISM. 


POLARITY OF THE MAGNETIC NEEDLE. 

BY 

ALEXANDER MEANS, M. D., D. D., LL. D. 

OXFORD, GEORGIA. 

Having been requested to furnish for this work an article 
explanatory of the Polarity of the Magnetic Needle, and 
an answer to the popular inquiry—Why does its arrow¬ 
head always point to the North?’’ this abbreviated essay 
is respectfully submitted. Magnetism, as it is now under¬ 
stood by the Scientific world, is a subject of profound and 
growing interest to the Chemist, the Philosopher, the 
Astronomer, the Navigator, the Magnetical and Telegraph 
Instrument Maker, and School Teacher. Its facts and phe¬ 
nomena, as discovered and traced within the last half cen¬ 
tury, give it a commanding position among those subtile, 
elementary forces which have within that period already 
revolutionized the commercial world, and which are now 
rapidly pushing their conquests into the hitherto retired 
and circumscribed domain of domestic and social life. 
Indeed, it is ascertained to be an ethereal medium of great 
power, activity and cosmical reign, not being confined in 
its manifestations to this earth alone—the sun himself—the 
great focal center of the system, giving palpable evidence 
of employing its agency in the production of signal results 
to be found in the planets and their satellites which revolve 
around him. A brief sketch of the history and modern 
progress of this Science, is all that circumstances will jus¬ 
tify. The simple fact, then, of the attractive, force of the 



80 


LAND SURVEYING. 


native Magnet, or Loadstone, which consists generally of 
the pro-toxide or black oxide of iron, was unquestionably 
known to Aristotle, 380 b. c. —to Pythagoras, 500 b. c., 
and to the great Grecian Bard, Homer, about 900 b. c.— 
but its property of polarization was not discovered until 
the twelfth century of the Christian era. Mr. Gilbert, of 
England, however, at the beginning of the seventeenth 
century (1600 A. D.) was the first to advance the bold 
hypothesis that our earth was a great magnet, having its 
greatest intensity at the two terrestrial poles, or the oppo¬ 
site “termini” of the ideal axis on which the earth re¬ 
volves. The dipping Of the Magnetic Needle, in advancing 
from the Equator to the Poles, was afterwards attributed 
to the supposed existence of a small magnet in the earth’s 
interior. It was subsequently suggested, however, by 
Tobias Mayer, that there must be two small magnetic bodies, 
so located in the body of the planet as to produce this re¬ 
markable result. 

About the year 1825, Ampere, of France, taught that the 
whole globe was magnetic, and that the intensity at the 
Poles, was the resultant of all the magnetic forces existing 
among its particles or molecules. He was also the first to 
maintain that electrical currents passing around the earth, 
would rationally account for all magnetic phenomena. 
This succinct historical .review of our Science must suffice 
for the purposes intended. We must now deal in more 
reliable data and more recent discoveries, and from these, 
according to Lord Bacon’s system of inductive philosophy, 
reasoning from ascertained and classified facts, to theories, 
and which is now universally adopted by all Scientists— 
we feel warranted to present the following satisfactory ex¬ 
planation of Terrestrial M ignetism, and consequently of 
the phenomena connected with the movements of the 
Magnetic Needle. And here, allow us to premise, that to 
furnish a clear and satisfactory exposition of Terrestrial 


TERRESTRIAL MAGNETISM. 


81 


Magnetism, its sources, its modes of action and its conse¬ 
quences would authorize an elaborate treatise at the hands 
of the writer. Nor would this be sufficient for the uniniti¬ 
ated, without the aid of diagrams or engravings, and the 
employment of a good Galvanic. Battery with appropriate 
appendages, such as Magnets, Helices, a small artificial 
globe, etc., etc. In supplying this article, however, for 
the student’s eye, our time, space and resources are all 
limited. We shall, therefore, attempt to simplify and con¬ 
dense, as far as practicable, leaving further demonstrations 
to the teacher. 

From the stand point occupied by modern Science it 
may now be enunciated that Light Heat , Electricity , Gal¬ 
vanism and Magnetism , all depend for the exhibition of 
their several functions upon the same ethereal, illimitable 
agent, only differing in its modes of action and forms of 
manifestation, and these, perhaps, mainly dependent upon 
the condition and properties of the bodies upon, or 
through which it acts, as solids, liquids and gases, of "dif¬ 
ferent chemical or material constitutions, and the circum¬ 
stances by which it is surrounded. Hence they are mutu¬ 
ally reproductive, each of the other. A few instances 
given will illustrate what we mean by this phrase, viz: 
Light developes Heat. For example : If equal volumes 
of Hydrogen and Chlorine gases are mixed in a glass jar, 
over a pneumatic cistern, and kept covered with black 
cloth, no action takes place between them. But if the 
sun’s rays are thrown in through a door or window from a 
reflected mirror directly upon the jar, although held at the 
distance of fifty or sixty feet from it, the black cover being 
removed , the two gases almost instantaneously combine 
with a powerful explosive reaction, resembling the report 
o r a pistol or musket, and Hydrochloric Acid alone is 
found in the j ir. Light generates Magnetism as in Miss 
Summerville’s experiment, in which a fine needle was 


82 


LAND SURVEYING. 


magnetized by holding it on the violet rays of the spec-1 
trum, thrown from a glass prism. Again Heat produces 
Light as in the case of'iron or other metals. A dull red 
Light is givetn off at about the temperature of 980 degrees' 
Farenheit—invisible except in the dark; a bright red 
light seen in the day at nearly 1160 degrees Farenheit and a 
full dazzling white light , at about 3000 degrees, Farenheit. 
Heat, too, generated by friction, turns a file into a mag¬ 
net, and ignites parlor matches which emit light. Elec¬ 
tricity also produces light, as in the spark lightning, the 
Aurora Borealis, through Edison’s horse shoe Carbon, 
etc. It also generates magnetism. For example: When 
a current is sent along a wrapped copper wire, wound 
spirally around a small bar of soft iron, whether straight 
or bent like the letter U, the bar is instantly converted 
into a magnet, the one extremity exhibiting Boreal 
(North) and the other Austral (South) M ignetism, deter¬ 
mined according to the course of the current. As soon as 
the current ceases to flow the iron is demagnetized. 

Once more, Galvanism, acting generally by plates of 
Zinc and Copper in contact with diluted Sulphuric Acid, 
generates powerful electrical currents accompanied with 
Heat, Light and Magnetism. This reciprocity of action 
or correlation of forces has given rise to at least four new 
departments of Science, viz : Electro magnetism, in which 
Electricity excites Magnetism ; Magneto-electricity , where 
Magnetism evolves Electricity ; Thermo-electricity * illus¬ 
trating the production of electrical phenomena by heat; 
and lastly, Electro-physiology ,** or the agency of the Elec¬ 
tric Fluid generated by the powers of life or the functions 
of living bodies, exerting its controlling influence upon 
the nervous system and the whole animal economy. 

*Th’s was discovered by Prof. Siebeck, of Berlin in 1822, to 
take place when two different metals, as German Silver (an alloy 
of Nickel with Copper) were laid in slight contact with Antimony; 


TERRESTRIAL MAGNETISM. 


83 


Signal instances of peculiar vital organism, adapted to 
the production, at will, of strong electric discharges, after 
the manner of a Galvanic Battery, are found in the tor¬ 
pedo, and Gymnotus Electricus, or the Electric Eel of 
Surinam, South America. This must suffice for the eye of 
the student. We need only add that the foregoing laws 
and their reported phenemona are all regarded as demon¬ 
strable with suitable apparatus and expert manipulation. 
And now to our main subject. It is to Thermo-elec¬ 
tricity, then, we are to attribute the phenomena manifested 
by the Magnetic Needle. As the earth revolves upon its 
axis from West to East, and the sun preserves a stationary 
position to the whole planetary train which surrounds him, 
consequently the sun’s track over the earth's surface must 
be from East to West, and the greatest intensity of his 
action must be within the equatorial belt where his rays 
are sent down vertically, viz: for 23^ degrees on each 
side of the Equator. Along this advancing line of way, 
therefore, his calorific rays generate thermo-electric cur¬ 
rents and polarize the particles of the oxides of iron, 
nickel, cobalt, ferruginous sand, and all other bodies 
capable of magnetic excitation, extending to a consider¬ 
able distance below the earth’s surface and in the neigh¬ 
borhood of that belt. So that a well balanced Needle, 
each arm from the center being of equal weight and sup¬ 
ported at the center by a sharp pointed iron or steel wire, 
fixed vertically in a pedestal of wood, will, at the magnetic 
Equator, assume and maintain a directly horizontal posi- 

or Silver with Antimony, etc., etc., and both heated at the point 
exjunction. The current flowing from the German Silver to the 
Antimony, etc. Indeed eighteen or twenty different metalic ar¬ 
rangements generate currents more or less intense. 

**See Dissertation on Elec'ro-physiology republidied in Medical 
andSurgic.il Journal, Atlanta, Ga., numbers December, 1877, and 
January, 1878, by A. Means, M. D., D. D., L. L. D. 




84 


LAND SURVEYING. 


tion, being equally attracted on both sides; so that its 
arrow head indicates Northern polarity and points toward 
the Pole in tb; Northern hemisphere which is really the 
South Pole of the earth. 



Now it will be found if this Needle is carried on North¬ 
ward its arrow-head will begin to dip earthward—the dip 
increasing for every degree of Latitude passed until having 
reached the terrestrial Pole, it will point directly down¬ 
ward and nearly in a line with the earth’s axis : because 
th q South side of the plain of the equatorial currents, now 
equidistant around the globe, produces its focal magnetic 
effect at the Pole and attracts the North or arrow-head of 
the Needle directly downward. If borne thence again 
onward toward the Equator, the dip becomes less and less 
for every degree, until at the Equator it becomes again 

















TERRESTRIAL magnetism. 


85 


horizontal. Let it then pass on to the other Pole and the 
feather end, or South Pole of the Needle, will begin to 
dip and continue to do so until at the Pole, the Needle 
will again become vertical, but its arrow-head now point¬ 
ing to the zenith and its feather end downward toward 
the earth’s center. 



In our Latitude the Temperate Zone, and especially in 
the Southern portion of that Zone, a Needle delicately 
poised will traverse with sufficient accuracy for the pur¬ 
poses of the Surveyor or Navigator. But in regions farther 
North the force of the dip must be counter-poised by a 
small movable pledget of lead, or a few turns of wire 
around the South end of the Needle to restore equilibrium at 
that Latitude. As the magnetic plain of the equatorial 
ring of currents varies, the Pole to which its axis points 
must manifest corresponding changes. Here we have Ihe 
probable cause of the " variations” of the magnetic Needle, 































86 


LAND SURVEYING. 


Eastward and Westward of the terrestrial pole in long 
periods of time. In the year 1600 the declination was 1 
Eastward. At about 1660 the Needle pointed to Zero (o) 
that is, North and South. After that period it commenced 
and continued a Westerly declination until 1818, (158 
years,) when the variation was found to be 24° 30'. Since 
then up to the present time it has been slowly returning. 

I must conclude by saying the effects of the magnetic j 
power of our earth, superinduced by electro-dynamic force, 
are observable in every day life. For example : A poker, 
tongs and many blacksmith tools, if set down with one 
end pointed to the earth, and especially if they happen to 
be standing in the magnetic meridian, are turned into 
magnets while in that position. 

Science within the last three-fourths of a century has ex¬ 
torted many invaluable secrets from the arcana of Nature. 
But how many more wonders are yet to reward her toila^ 
other generations must report. But they are all helJP 
in reserve until the Divine Ruler of the Universe shall dis 
cover that advancing Christian civilization is ready t 
receive them, and they shall be evolved from his exhaust 
less resources through the agency of other Franklins am* 
Morses and Fultons. M 





LAWS OF GEORGIA RELATING TO COUNTY 
SURVEYORS. 


BY 

J. B. ESTES, Attorney at Law, 

GAINESVILLE, GA. 

§i. (566.) How elected. —County Surveyors are elected, 
commissioned, qualified and removed as Clerks of the 
Superior Courts are, and hold their office for two years. 

§2. (1319.) When elected. —Ordinaries, Clerks of the 
Superior Courts, Sheriffs, Coroners, Tax Collectors, Tax 
Receivers, County Surveyors, and all county officers, shall 
be elected on the first Wednesday in January of the years 
n which, under the Constitution and laws of this State, 
elections should be held to fill such offices, beginning on 
.he first Wednesday in January, 1873. 

§3. (1320.) Official term of County Officers. —The terms 

• jf the present Sheriffs, Clerks of the Superior Courts, Tax 
| Collectors, Tax Receivers, County Treasurers, County 
‘.'Surveyors and Coroners shall begin on the first day of 
I January, 1873, and expire on the first day of January, 1875. 

• Vnd all succeeding terms of said officers shall begin on the 
first day of January, and expire on the first day of January 

• wo years next thereafter. 

1 §4- (567.) Failure to elect. —In case there is a failure to 
| lect a person who is commissioned and qualified at the 
1 egular time, or a vacancy occurs, the Ordinary must ap¬ 
point such Surveyors until the vacancy is filled according 
o law. 

§ 5 * (56S ) When appointed by the Court. —If a County 
urveyor derives his authority from appointment, he needs 


88 


LAND SURVEYING. 


no commission beyond the order of such Ordinary entered 
on his minutes, of which appointment the Governor of the 
State must be informed without delay. 

§6. (569.) Oath and Bo?id .—Before entering on the 
duties of his office, besides the oath required of all civil 
officers, he must take the following: 

“ I . . . swear that I will, to the best of my skill and 
knowledge, discharge the duties of Surveyor of ... . 
County, and that I will not admeasure, survey or lay out 
any land in my capacity as such, or knowingly permit or 
cause it to be done, without a warrant first obtained for 
that purpose, so help me God,” 


He shall also at the same time give bond and security 
in the sum of one thousand dollars. 

§7. (570.) May be removed. —Whether appointed or 
elected, besides the causes of removal which apply to all 
officers, he may be removed by the Ordinary for want of 

1 

capacity, on the same proceeding before him, and by him 
to be decided, that officers are removed in the Superior 
Courts. 

§8. (571.) One for each county. —There must be one 
for each county, and he is empowered to appoint one or 
more assistants or deputies, for whose conduct he is respon-i 
sible. 

§9. (572.) Must take an Oath. —When such an assistant J 
is appointed he must take the same oath the Surveyor* 
takes, and the fact of the appointment must, at the same > 
time, be entered on the minutes of the Ordinary. 

§10. 1573 ) Office , where kept. —The County Surveyor! 
may keep his office at his place of abode. 

§11. ( 574 .) Duties. —It is his duty— 

1. To punctually observe and carry into effect all suctji 



LAWS RELATING TO COUNTY SURVEYORS. 89 


orders as he may receive from the Surveyor General or 
oilier officer who may lawfully command him. 

2. To admeasure and lay off dower, to partition land, 
to make re-surveys, to give plats of all surveys and to ad¬ 
minister all oaths required by law in such cases. 

3. To survey county lines and district lines, or other 
surveys in which his county may be interested, whenever 
required by the Ordinary. 

4. To execute all surveys required by the rule of any 
Court of competent jurisdiction. 

5. To keep a well bound book in which shall be entered 
plats of all surveys made by him, with a minute of the 
names of the chain-bearers, when executed, by whose order 
and to whom plat delivered, if any; which book shall 
belong to his office and be turned over to his successor, 
and when full shall be deposited in the office of the Ordi¬ 
nary. 

§12. (575.) Fees ,—When surveys are made for private 
or corporate benefit, the fees are to be paid by the person 
or persons, or corporation who orders the survey; when by 
order of the Ordinary, out of the county funds; and when 
by rule of Court, unless otherwise agreed upon, they are 
to be taxed in the bill of costs, and shall have the effect 
of a judgment lien upon the land surveyed if not paid by 
the party bound for costs. 

§ I 3 - (576-) Survey between Counties. — When a survey 
is made by agreement, or in compliance with the law be¬ 
tween two or more counties, the County Surveyor who 
performs the survey is to be paid by his county, which 
must collect from the other counties their proportion. 

§14. (577 ) Payment of Fees. —If, after a County Sur¬ 
veyor has made a survey for any person, who neglects to 
piy him. such surveyor, upon making oath before the 
Ordinary of his county of the.performance of such service 


00 


LAND SURVEYING. 


and its value, such Ordinary shall issue a fi. fa., in the name 
of the Ordinary for the use of such Surveyor against such ; 
defaulter, who may defend himself therefor, in the same : 
manner as persons against whom executions issue who de¬ 
tain county funds. 

§15. ( 578 .) Surveys when Evidence. —Surveys or plats 
of land made by the County Surveyor, under order of 
Court, and on notice to all the parties, of lands within his 
county, signed by him officially, and stating the contents, 
courses, distances, of any land surveyed by him, are pre¬ 
sumptive evidence of the facts, if all the requisites of the 
law touching such surveys and the reports thereof are com¬ 
plied with. 

§16. ( 579 .) Whci'e there is no Surveyor. —When there 
is no County Surveyor, any competent person, a citizen of 
the county, may perform his duties when specially required, 
if first sworn to do the same skillfully, faithfully and im¬ 
partially, to the best of his knowledge ; or in default of such 
person the County Surveyor of an adjoining county may 
officiate. 

§17. (580.) Persons acting. —Persons performing such 
service are on the same footing as County Surveyors as to 
the special service rendered, and are personally liable as 
such surveyors are officially. 

§18 (581.) False survey —When any County Surveyor 
or other person acting as such, has knowingly surveyed 
land as vacant land which is not, or so made any other 
false survey, he is guilty of a misdemeanor, and on indict¬ 
ment and conviction shall be imprisoned not longer than 
six months. 

§19. (2371.) Duty of, in case of head rights. —If no 
caveat is filed, or if filed, is not sustained, the said Ordi¬ 
nary shall issue a warrant directed to the County Surveyor 
requesting him to view the land alleged to lie vacant, and 





LAWS RELATING TO COUNTY SURVEYORS. 91 


if upon due examination of the adjoining surveys he is 
satisfied that the same is vacant, to make an accurate sur¬ 
vey and plat of the same, and return the plat to the said 
Ordinary with his official certificate as to its accuracy, the 
time of survey, and his opinion that the same is vacant. 
Notice of the time of survey shall be given to all the own¬ 
ers of adjacent lands, resident within the county, by the 
County Surveyor at least ten days before the time appointed, 
and like notice of any delay or postponement of the time. 

§20. (2372) His certificate if the land is granted .—If 
the County Surveyor shall be satisfied that the land is not 
vacant, he shall certify the fact to the Ordinary issuing the 
warrant, with the name of the grantee or grantees, to whom, 
in his opinion, the same has been granted, and return the 
warrant to the Ordinary. The applicant, if he sees proper, 
may take issue upon such return, and such issue shall be 
transmitted to the Superior Court, in like manner as a 
caveat, to be there tried. The Superior Court shall give 
notice in the most practicable manner to the owner or 
owners of the old grant or grants of the pendency of such 
issue before the trial of the same. If the issue is found for 
the applicant the survey shall proceed. 

§21. (2373.) False return by Surveyor .—Any County 
Surveyor who shall knowingly or without due precaution, 
certify as vacant, land covered by former grant, shall be 
liable, with his sureties on his bond, to the owner of such 
land for double the value of the same, at any time before 
the trial of the cause. 

Explanation.— The number with section mark (g) prefixed is 
the section of this chapter. The figures included in brackets at the 
beginning of each section refer to the section of the Revised Code 
of Georgia, where the same is found. 

Decisions of Supreme Court of Georgia on foregoing 
sections of law. 


92 


LAND SURVEYING. 


Rule of survey taken out pending an action of Eject¬ 
ment : 28 Ga., 465. 

Certificate of County Surveyor as evidence: 21 Ga., 
113. Requisites of warrant: 14 Ga., 349; 29 Ga., 754; 
33 Ga., 296. Amendment of: 29 Ga., 753. 



■ 



TEXAS LAND SYSTEM AND LAND SUR¬ 
VEYING. 


BY 

Col. WARREN DOUGLAS, 

PRACTICAL SURVEYOR, CLEBURNE, JOHNSON COUNTY, TEXAS. 

Texas land surveys and grants are based upon land cer¬ 
tificates authorizing the grantee to have surveyed out of 
the public domain, by any legally authorized surveyor, so 
much land ; and upon the return of the certificate, together 
with the field notes of the land surveyed, to the General 
Land Office of the State, the holder, all things being regu¬ 
lar and correct, is entitled to a grant, or letter patent to 
the land de cribed in the field notes. Legally authorized 
surveyors of Texas are District Surveyors and their Depu¬ 
ties. Originally, the State was divided by law into a very 
few districts, embracing large extents of territory; each 
District Surveyor was required to keep a map of his district 
and a record of all surveys made by him, or his deputies, 
returning the original field notes to the Commissioner of 
the General Land Office, to whom all were subordinated. 
Afterwards, as the country became populated, each county 
was authorized by law to erect itself into a land district, 
by having a transcript from the records of its original 
district, of all the surveys within its own limits, taken at 
its own expense. 

Many counties have availed themselves of this privilege, 
and a surveyor of a land district comprising one county, 
is called indifferently a district or a county surveyor and 
may have his deputies. But in Texas, the duties of a dis¬ 
trict or county surveyor have reference to the Public 
Domain only; the dividing or partitioning of surveys and 


94 


LAND SURVEYING. 


the determination of boundaries being left to mutual con- ; 
sent of parties or to surveyors appointed by Decrees of j 
Courts. Owing to the system of land surveying adopted j 
by the Republic and State of Texas, or rather followed out 
by them, for it was practiced by Spanish and Mexican 
authority, and to the further consideration that at an early 
day, and even now, on the extreme frontier, surveying, 
in the wilds of Texas, was extremely dangerous, that Texas 
land and land certificates were regarded as of trifling value, 
often the fees for entering and surveying land amounting 
to almost the full value of the certificate, and that each 
surveyor, or deputy, worked in the field without actual 
supervision or control, little uniformity could be expected, 
and in fact, little is to be found. The writer has found 
in the same county a difference of nearly four degrees in 
the running of different surveyors, or, in other words, varia¬ 
tions of from 8° 30' all the way up to 12 0 , the true magnetic 
variation, in this section, being about 9 0 40' E., and errors, 
(usually excesses) of measurements running from 1 to 10 . 
per cent in the length of lines. As the principal duty of 
the present and future surveyors will be to re-establish the 
boundaries of surveys made long before, and as he must 
follow the footsteps of the original surveyor, it becomes ) 
his business rather to ascertain what variation of his needle 
will cause his compass to follow the courses indicated by 
the calls in his field notes, in the particular survey upon 
which he is called to work, than to determine what is the • 
true magnetic variation. For this purpose he will first . 
train his compass by running first on the best marked line 
of the survey, or from one well established corner to an- \ 
other, or to some distinct and indisputably marked point 
in the boundary, as a fore and aft tree. Here the surveyor 
needs a rule for correcting errors of this kind which are 
usually small, or within one or two degrees. I offer the 
following one, not as being the best or shortest, but as 


TEXAS LAND SURVEYING. 


95 


easy to remember, and in reach of the common arithme¬ 
tician and easily reduced by him to practice. 

RULE. 

Consider the distance run the radius of a circle, and the 
error a part of its circumference. Calculate the circum¬ 
ference and divide by 360 and you have the value of a 
degree of said circle; divide this by, or into your error 
and you have it, the error, expressed in degrees or frac¬ 
tions of a degree. For example: 

Suppose a distance run of 700 varas, error 13 varas. 
Then 700 X 6^=4400-^-360= 12!= i°. But error is 13 
equal to 1^ degree=i T 1 g° or i° 4' nearly. 

This formula though not absohitely correct, is more 
nearly so than any practical adjustment of the compass 
can be, and will give satisfactory results. Having set the 
compass now i°-4' to the right or left as the case may be, 
continue to the next certain point in the same line. If 
you find yourself again in error you may suspect a false 
run or crook in the original line: note your error at this 
point, move into the true line and proceed as before, and 
so on, until the termination of the line is reached, at which 
note error both in course and distance from the initial 
point, if it be a fixed and well ascertained position. Now 
you will have the data to calculate the true course, from 
the beginning to the termination of the line and to find 
the true position of the intermediate marks with reference 
to it. If they be upon this line, or alternately to the right 
and left, readjust your compass by the above formula so as 
to run correctly the whole line and assume that to be the 
true course of that line, and your variation so ascertained 
as the one likely to follow the remaining lines of that par¬ 
ticular survey. But if the intermediate marks or a number 
of them indicate a straight line on a course diverging from 
the line from the corner, you will suspect a mistake; either 


96 


LAND SURVEYING. 


the surveyor you are trying to follow has diverged from a 
line he has called for, and followed by supposition, or de¬ 
scribed a corner taken, from other field notes and which he 
did not actually run to^md establish, or some subsequent 
surveyor has run and marked a line in error. Consider 
what would most likely solve the difficulty. Adopt the 
one line or the other as your base and proceed as before with 
your next line. If in this you find yourself in error as be¬ 
fore, note carefully the error, remembering that there is 
most likely parallelism in the opposite lines of a survey, 
even though the angles be not accurately measured. 

In resurveys, follow the marks specified in your field 
notes and respect corners originally made, if they can be 
identified, regardless of course and distance. In re-estab¬ 
lishing old corners, make the unknown correspond to and 
agree with the known corners or mirk as actually situated 
on the ground. When one line is known or tracable, estab¬ 
lish its opposite if untracable, by parallelism with it. 
When but one line of a survey may be traced, establish all 
others in harmony with it as to magnetic variation. When 
only one course is known or can be identified, run in 
harmony with surrounding surveys as to magnetic variation, 
especially if made by the same surveyor. But when this 
cannot be ascertained, run according to the true variation 
and observe distance strictly. 

PARTITION. 

In subdividing lands, first ascertain all that can be known 
as to actual boundaries of the survey and the gain or loss 
in actual area. If the parties to the partition are mutually 
interested in it as a whole, as in case of partition among 
heirs or partners, the gain or loss is to be distributed among 
the several parts “pro rata.” But if one ora number 
have purchased a specific amount of land from another, 
then said amount is to be accurately laid out; the gain or 


TEXAS LAND SURVEYING. 


97 


| loss remaining with the vendor. Partition lines should 
i maintain exact parallelism with original boundaries. 

ERRORS. 

A few remarks now on occasional or accidental errors 
in the lines of Texas Surveyors. 

ist. A false run or deflection of course. This may hap¬ 
pen in two ways— -first, in running lines by natural objects, 
the eye being removed for an instant from the object, an¬ 
other similar in appearance, but different in fact^S mis¬ 
taken for the true object and the remainder of the course 
actually run, be in error by the distance of the false object 
from the true line. Secondly , The fastening of the vernier 
may become loosened and the “ set ” of the compass dis¬ 
arranged and escape the notice of the surveyor. This, of 
course, makes bad work. 

2d. Marking is sometimes done in error, by the surveyor 
departing slightly from his course to avoid obstructions, 
followed by the marker. This is an irregularity of frequent 
occurrence in Texas surveying; it is of easy detection and 
comparatively harmless in its consequences. 

3d. Clerical errors are of frequent occurrence, the 
most common being the use of a wrong initial letter in in¬ 
dicating the course of a line, as S. for N., E. for W. and 
vice versa. These mistakes are usually apparent and fla¬ 
grant and when they apply to the course or bearings given 
in field notes from corners of a survey to witness trees or 
monuments, they are not palpable and cannot be disre¬ 
garded or set asitfe except by the strongest evidence in 
other marks made and described in the field notes. Unfor¬ 
tunately, this kind of mistake is but too frequent. Some¬ 
times, the figures expressing degrees are transmuted with 
those expressing distance, as N. 27, W. 27 varas becomes 
N. 27, VV. 47 varas. Therefore too much care cannot be 
exercised in taking field notes. 



98 


LAND SURVEYING. 


MEASUREMENTS. —Varas, Labors and Leagues. ' j 

These are terms of Spanish land measurement, lineal and 
square, and were used in giving and surveying land grants | 
in Texas under Spanish and Mexican authority. Upon the 
accession of Anglo American authority, the English and i 
American square measure of acres and sections was introdu- ! 
ced (perhaps as being more comprehensible to the Ameri- j 
can mind) but owing to the great inconvenience involved 
in a change of the unit of lineal measure, the Texas Land 
Office still retains, and no doubt will ever retain, the Vara 
as the unit of length. Hence, we have in Texas, land 
grants expressed in square varas, labors (pronounced la- 
bdres) and leagues, their multiples and fractions, and oth¬ 
ers expressed in acres and sections with their multiples 
and fractions, but at the same time our Texas land system 
knows no unit of lineal measure save the vara. All sur¬ 
veys returned to the General Land Office must have their 
dimensions expressed in varas; as, for instance, a square} 
section of 640 acres will be described as being in the 
length of each boundary 1900 varas instead of one mile, ! 
or so many rods or yards: 

TABLE OF SPANISH LAND MEASURE. 


i Vara ..33 J inches; 

1 Acre.5646 square varas—4840 square yards. 

1 Labor.1,000.000 square varas—177 acres. 

y 3 League .... 8,333,333.0c square varas—1476 acres. 
1 League.25,000,000 square varas—4425 acres. 


1 League and Labor, 26,000,000 square varas—4605 acres. 

To find the number of acres in a given number of square 
varas, divide by 5646—reject fractions. 

It will be seen from the above table that the vara is 
equal to thirty-three and one-third inches (English) or, 
3 varas=ioo inches. Hence, to reduce varas to inches, 








TEXAS LAND SURVEYING. 


99 


annex two ciphers and divide the result by 3. To reduce 
varas directly to yards annex two cyphers and divide by 
108. 

The Labor, square measure, is equal to 1,000,000 square 
varas, or, a square survey of 1,000 varas square. It is 
equivalent to 177 acres. 

The League, square measure, is equal to 25 labors, or a 
square survey of 5.000 varas to the side, or to 4425. 

The equivalents of varas, etc., in miles and acres are 
only proximately used and passed in Land offices and gen¬ 
eral practice as counts. 

The Official Scale in General Land Office for platting 
is 4,000 varas to the inch. Double scale is allowed in 
plats returned with field notes. 

Chains in Texas are of 10 or 20 varas in length, and 
should have five links to the vara. Fractions of varas are 
expressed in tenths , not links. 

The primary principles of surveying, platting and get¬ 
ting area are the same in Texas as elsewhere, with the ap¬ 
plications and requirements here set forth. 




Advice to Young Surveyors. 


It may not be considered improper in the author to ven¬ 
ture a word or two of useful advice before parting with 
the student. 

In selecting assistants in your field work never call to 
your aid John Barleycorn, sometimes called whisky , bran¬ 
dy , and rum. John is thought by many to be a pleasant 
and important companion on works of this kind, but by 
his might the strong man has fallen and the promising 
young man has found an early grave. If you take him in 
your employ your bearings will very likely be wrong, your 
field notes incorrect, the platting a disgrace and your rep¬ 
utation ruined. He can never do you the least service in 
any department of the work, but is sure to destroy your 
usefulness as a Surveyor. Therefore let one who wishes 
you well beg you to shun all such assistants. 




USEFULTABLES 


LENGTH OF EACH SIDE OF A SQUARE CONTAINING 


1 Acre in 

feet, 

fractions 

rejected 

2 Acres 

n 

u 

u 

3 Acres 

u 

n 

ii 

4 Acres 

u 

(( 

a 

5 Acres 

u 

a 

ii 

6 Acres 

ii 

a 

ii 

7 Acres 

.< 

ll 

ii 

8 Acres 

ll 

ll 

.< 

0 Acres 

a 

ii 

ii 

10 Acres 

(( 

a 

ii 


208 

205 

861 

417 

466 

511 

552 

590 

626 

660 


LAND MEASURE. 

In England and the United States the acre consists of 160 square 
rods, or 4,840 square ya r ds, or 43,560 square feet. In Scotland 
the acre is 6,840 square yards. 


MEASURE OF DISTANCES. 

A mile is 5280 feet; 1760 yards ; 320 rods ; or 80 chains. 

A rod is. 16 | feet. 

A fathom is. 6 feet. 

A league is. 3 miles. 

A cubit is. 2 feet. 

A great cubit is. 11 feet. 

A hand (horse measure) is.. - 4 inches. 

A palm is. 3 inches. 

A span is. 10 i inches. 

A pace is. 3 feet. 


QUANITY OF SEED USUALLY SOWN TO AN ACRE. 


Herd’s grass, or Tim* 


othy . . . 


1 bus. 

Red Top . . . 


1 bus. 

Red Clover. . 

. . 6 to 

10 lbs. 

White Clover . 

. . 5 to 

8 lbs. 

Lucerne . . . 


10 lbs. 

Orch. Grass . 

. . 1 to 

11 bus. 

Blue Grass . . 

.. 11 ° 

1 bus. 

Rye Grass . . 

. . 1 to 

11 bus. 

Wheat .... 


2 bus. 

Barley .... 

. . 11 to 

2 bus. 

Buckwheat . . 

. . 1 to 

ll bus. 


Carrot. 


to 3 

lbs. 

Beet. 


to 6 

lbs. 

Parsnip .... 

. 3 

to 5 

lbs. 

Onion. 


to 6 

lbs. 

Ruta Baga . . . 

. 

1 

lb. 

Turnip. 


to ll 

lbs. 

Beans . 

. 11 

to 2 

bus. 

Peas. 

. 11 

to 2 

bus. 

Oats. 

. 21 

to 3 

bus. 

Rye ...... 


to 11 

bus. 

Millet. 

• 2 

to 4 

bus. 





































102 


USEFUL TABLES. 




QUANTITY Of CORN REQUIRED TO PLANT AN ACRE, FIVE GRAINS IN 

THE HILL. 


3 feet by 2. 18 qts 

3 £ feet by 2.10 qts. 

3 feet by 4 . 7 qts. 


3 fret by 3 . . . . .12 qts. 

3 f feet by 3 .8 qts. 

4 feot by 4 .6 qts. 


TIIE NUMBER OF PLANTS PER ACRE, AT GIVEN DISTANCE. 


1 foot. . . . 

. 43,560 

6 feet . . . 

. . . . . .1,210 

\\ feet . . . . 


9 feet . . . 


2 feet. . . . 


12 feet . . . 


2£ feet . . . . 


15 feet . . . 


3 feet. . . . 


18 feet . . . 


4 feet. . . . 

. 2,722 

20 feet . . . 

. 109 

5 feet, . , . 

...... 1,742 

25 feet . . . 

. 00 

will contain 0,050 

One acre of Tobacco set 4 feet 

by 2£ distant, 


plants. Most growers prefer 3 ^ feet by 2 , which gives 0 , 223 . plants 
to one acre. 


























RECOMMENDATIONS. 


Uiveksity of Georgia. 

Athens, Nov. 15 th, 1880 . 

I have examined the manuscript of “Caldwell’s Practical Sur 
veying,” and believe it just such a work as will meet the wants of 
the large class of Surveyors and students who desire to learn this 
art practically and in a short time. I have long wished for such a 
book to meet the wants of our average County Surveyors. By his 
request, I have furnished several chapters on practical methods 
which are the result of my long experience as a Surveyor. The 
chapter on 11 Annual Variation of the Needle ,” is so important to 
the average County Surveyor, that I am glad to have the opportu¬ 
nity of presenting the practical method of determining it for any 
particular locality. And hooe it will be the means of preventing 
lawsuits about land lines in future. 

I hope to see the book meet with a heavy sale. 

WILLIAMS RUTHERFORD, A. M., 
Prof. Mathematics , University of Ga. 


Gainesville, Ga., Nov. 17 th, 1880 . 

I have examined the manuscript of Caldwell’s Practical Survey¬ 
ing, and find it to be a work eminently fitted to fill the place it is 
designed to occupy. There has long been a need of just such a work— 
it is clear, concise and practical. It will be an excellent book to 
put into the hands of a boy that has a fair knowledge of arithmetic, 
and even old surveyors will find in it much useful information con¬ 
densed into a small space. 

C. B. LaHATTE, 

President of the Methodist College , Gainesville , Ga. 





INDEX 


Pa^e. 

CHAPTER I.—Definitions. 9-10 

Primary principles,. 10 

Angles,. 10 

Triangles. 10 

Quadrilaterals,. It 

Circles,. 12 

CHAPTER II.—Instruments.15-20 

Compass, . 15 

Transit. 18 

The Chain,. 19 

CHAPTER III.—Howto Chain,.21-22 

How t) Chain,. 21 

CHAPTER IV.—Field Work,.....23-26 

Compass Surveying,. 23 

CHAPTER V.—Magnetic Variation,.27-32 

Variation of the Needle,. 27 

CHAPTER VI.—Passing Obstacles,.33-36 

A Pond,. 33 

First Method. 34 

A River—Second Method,. 35 

With a Compass and Chain. 35 

CHAPTER VII.—Random Lines. 37-39 

First Method. 37 

Rule. 38 

Second Method. . 39 

CHAPTER VIII.— Field Notes.40-45 

Instruction... 41 

I lustration. 42 

Rivtrline. 44 

CHAPTER IX.—Platting.46-53 

Remarks. 46 

Two Methods. 46 

The Scale. 46 

The Protractor. 47 





































INDEX. 


105 


CHAPTER IX.—Continued. 

The Dividers. 

To Plat with the Protractor. 

To Close the Plat. 

With a Scale of Chords. 

With a Scale of Chords*. 

With the Protractor,. 

CHAPTER X.—Calculating Area. 

Squares, Rectangles, etc.,. 

Table of Square Measure. 

Trapezoid. 

Triangle. 

Offsets . 

Circles... 

Area to find Diameter. 

An Ellipse. 

By Stepping. 

CHAPTER XI.—Dividing Lands. 

A Square. 

A Rectangle. 

A Triangle. 

CHAPTER XII.—Surveying by Tangents. 

Illustration. 

CHAPTER XIII.—Altitudes and Heights 

Illustration . 

APPENDIX. 

Polarity of the Needle.... 

Duties of County Surveyors. 

Texas Land System and Surveying. 

Advice to Young Surveyors. 


. 47 

. 49 

. 50 

50 
. 51 

. 53 

,54-66 
. 55 

, 56 


57 

61 

62 

64 

64 

65 
,67-72 

67 

, 68 
69 
73-75 
74 
76-78 
77 
79 
,79-86 
,87-92 
.93-99 
100 
































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